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【330310】2020年湖北省武汉市中考数学试题

时间:2025-02-09 10:50:53 作者: 字数:25883字

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 湖北省武汉市2020年中考数学真题

一、选择题

1. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的相反数是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B. 2 C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】B

【解析】

【分析】

根据相反数的性质可得结果.

【详解】因为-2+2=0,所以﹣2的相反数是2

故选B

【点睛】本题考查求相反数,熟记相反数的性质是解题的关键 .

2.式子 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在实数范围内有意义,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 取值范围是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】D

【解析】

【分析】

由二次根式有意义的条件列不等式可得答案.

【详解】解:由式子 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在实数范围内有意义,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选D

【点睛】本题考查的是二次根式有意义的条件,掌握二次根式的被开方数为非负数是解题的关键.

3.两个不透明的口袋中各有三个相同的小球,将每个口袋中的小球分别标号为123.从这两个口袋中分别摸出一个小球,则下列事件为随机事件的是(

A. 两个小球的标号之和等于1 B. 两个小球的标号之和等于6

C. 两个小球的标号之和大于1 D. 两个小球的标号之和大于6

【答案】B

【解析】

【分析】

随机事件是指在某个条件下有可能发生有可能不会发生的事件,根据此定义即可求解.

【详解】解:从两个口袋中各摸一个球,其标号之和最大为6,最小为2

选项A:“两个小球的标号之和等于1”为不可能事件,故选项A错误;

选项B:“两个小球的标号之和等于6”为随机事件,故选项B正确;

选项C:“两个小球的标号之和大于1”为必然事件,故选项C错误;

选项D:“两个小球的标号之和大于6”为不可能事件,故选项D错误.

故选:B

【点睛】本题考查了随机事件、不可能事件、必然事件的概念,熟练掌握各事件的定义是解决本题的关键.

4.现实世界中,对称现象无处不在,中国的方块字中有些也只有对称性,下列汉字是轴对称图形的是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】C

【解析】

【分析】

根据轴对称图形的定义“在平面内,一个图形沿着一条直线折叠,直线两旁的部分能够完全重合的图形叫做轴对称图形”逐项判断即可得.

【详解】A、不是轴对称图形,此项不符题意

B、不是轴对称图形,此项不符题意

C、是轴对称图形,此项符合题意

D、不是轴对称图形,此项不符题意

故选:C

【点睛】本题考查了轴对称图形的定义,熟记定义是解题关键.

5.下图是由4个相同的正方体组成的立体图形,它的左视图是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】A

【解析】

【分析】

根据左视图的定义即可求解.

【详解】根据图形可知左视图为

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选A

【点睛】此题主要考查三视图,解题的关键是熟知左视图的定义.

6.某班从甲、乙、丙、丁四位选中随机选取两人参加校乒乓球比赛,恰好选中甲、乙两位选于的概率是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】C

【解析】

【分析】

画出树状图展示所有12种等可能的结果数,再根据概率公式即可求解.

【详解】画树状图为:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

P(选中甲、乙两位)= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选C

【点睛】本题考查了列表法或树状图法:通过列表法或树状图法展示所有等可能的结果求出n,再从中选出符合事件AB的结果数目m,然后根据概率公式求出事件AB的概率.

7.若点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的图象上,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的取值范围是(

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】B

【解析】

【分析】

由反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,可知图象经过第二、四象限,在每个象限内,yx的增大而增大,由此分三种情况①若点A、点B在同在第二或第四象限;②若点A在第二象限且点B在第四象限;③若点A在第四象限且点B在第二象限讨论即可.

【详解】解:∵反比例函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

图象经过第二、四象限,在每个象限内,yx的增大而增大,

若点A、点B同在第二或第四象限,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

a-1a+1

此不等式无解;

若点A在第二象限且点B在第四象限,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

y1y2,可知点A在第四象限且点B在第二象限这种情况不可能.

综上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的取值范围是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选:B

【点睛】本题考查反比例函数的图象和性质,熟练掌握反比例函数的图象和性质是解题的关键,注意要分情况讨论,不要遗漏.

8.一个容器有进水管和出水管,每分钟的进水和出水是两个常数.从某时刻开始 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 内只进水不出水,从第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 到第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 内既进水又出水,从第 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 开始只出水不进水,容器内水量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (单位: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> )与时间 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (单位: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> )之间的关系如图所示,则图中 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

A. 32 B. 34 C. 36 D. 38

【答案】C

【解析】

【分析】

设每分钟的进水量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,出水量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,先根据函数图象分别求出bc的值,再求出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时,y的值,然后根据每分钟的出水量列出等式求解即可.

【详解】设每分钟的进水量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,出水量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

由第一段函数图象可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

由第二段函数图象可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

则当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

因此, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选:C

【点睛】本题考查了函数图象的应用,理解题意,从函数图象中正确获取信息,从而求出每分钟的进水量和出水量是解题关键.

9.如图,在半径为3的⊙O中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是直径, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是弦, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的中点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> .若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的中点,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的长是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

A.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> B.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> C.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> D.  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】D

【解析】

【分析】

连接DODADC,设DOAC交于点H,证明△DHE≌△BCE,得到DH=CB,同时OH是三角形ABC中位线,设OH=x,则BC=2x=DH,故半径DO=3x,解出x,最后在Rt△ACB中由勾股定理即可求解.

【详解】解:连接DODADCOC,设DOAC交于点H,如下图所示,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

D <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的中点,∴DA=DC,∴D在线段AC的垂直平分线上,

OC=OA,∴O在线段AC的垂直平分线上,

DO⊥AC,∠DHC=90°

AB是圆的直径,∴∠BCA=90°

EBD的中点,∴DE=BE,且∠DEH=∠BEC

∴△DHE≌△BCE(AAS)

DH=BC

OAB中点,HAC中点,

HO是△ABC的中位线,

OH=x,则BC=DH=2x

OD=3x=3,∴x=1

BC=2x=2

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> Rt△ABC中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选:D

【点睛】本题考查了圆周角定理、三角形全等、勾股定理等,属于综合题,熟练掌握其性质和定理是解决此题的关键

10.下列图中所有小正方形都是全等的.图(1)是一张由4个小正方形组成的“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ”形纸片,图(2)是一张由6个小正方形组成的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片.把“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ”形纸片放置在图(2)中,使它恰好盖住其中的4个小正方形,共有如图(3)中的4种不同放置方法,图(4)是一张由36个小正方形组成的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片,将“ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ”形纸片放置在图(4)中,使它恰好盖住其中的4个小正方形,共有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 种不同放置方法,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值是(

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

A. 160 B. 128 C. 80 D. 48

【答案】C

【解析】

【分析】

先计算出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片中共含有多少个 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片,再乘以4即可得.

【详解】由图可知,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片的个数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (个)

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故选:C

【点睛】本题考查了图形类规律探索,正确得出在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 方格纸片的个数是解题关键.

二、填空题

11.计算 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的结果是_______.

【答案】3

【解析】

【分析】

根据二次根式的性质进行求解即可.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> =3

故答案为3.

【点睛】本题考查了二次根式的性质,熟练掌握二次根式的性质 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是解题的关键.

12.热爱劳动,劳动最美!某合作学习小组6名同学一周居家劳动的时间(单位: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ),分别为:433556.这组数据的中位数是________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【解析】

【分析】

根据中位数的定义即可得.

【详解】将这组数据按从小到大进行排序为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

则这组数据的中位数是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了中位数的定义,熟记定义是解题关键.

13.计算 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的结果是________

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【解析】

【分析】

根据分式的减法法则进行计算即可.

【详解】原式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了分式的减法运算,熟记运算法则是解题关键.

14.在探索数学名题“尺规三等分角”的过程中,有下面的问题:如图, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是平行四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的对角线,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的大小是________

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】26°

【解析】

【分析】

设∠BAC=x,然后结合平行四边形的性质和已知条件用x表示出∠EBA、∠BEC BCE BEC DCA、∠DCB,最后根据两直线平行同旁内角互补,列方程求出x即可.

【详解】解:设∠BAC=x

平行四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的对角线

DC//AB,AD=BC,AD//BC

∴∠DCA=∠BAC=x

AE=BE

∴∠EBA =∠BAC=x

∴∠BEC=2x

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

BE=BC

∴∠BCE=∠BEC =2x

∴∠DCB=∠BCE+∠DCA=3x

AD//BC <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

∴∠D+∠DCB=180°,即102°+3x=180°,解得x=26°

故答案为26°

【点睛】本题主要考查了平行四边形的性质、等腰三角形的判定和性质,运用平行四边形结合已知条件判定等腰三角形和掌握方程思想是解答本题的关键.

15.抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为常数, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> )经过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两点,下列四个结论:

一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的根为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

若点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在该抛物线上,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

对于任意实数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,总有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

对于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的每一个确定值,若一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为常数, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> )的根为整数,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值只有两个.

其中正确的结论是________(填写序号).

【答案】①③

【解析】

【分析】

根据二次函数与一元二次方程的联系即可得;②先点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 得出二次函数的对称轴,再根据二次函数的对称性与增减性即可得;③先求出二次函数的顶点坐标,再根据二次函数图象的平移规律即可得;④先将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向下平移 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 个单位长度得到的二次函数解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再根据二次函数与一元二次方程的联系即可得.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 经过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两点

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的根为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则结论①正确

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 抛物线的对称轴为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时的函数值与 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时的函数值相等,即为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时,yx的增大而减小

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则结论②错误

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

则抛物线的顶点的纵坐标为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向下平移 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 个单位长度得到的二次函数解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

由二次函数图象特征可知, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的图象位于x轴的下方,顶点恰好在x轴上

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 恒成立

则对于任意实数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,总有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,结论③正确

将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向下平移 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 个单位长度得到的二次函数解析式为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

函数 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 对应的一元二次方程为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

因此,若一元二次方程 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的根为整数,则其根只能是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

对应的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值只有三个,则结论④错误

综上,结论正确的是①③

故答案为:①③.

【点睛】本题考查了二次函数的图象与性质(对称性、增减性)、二次函数图象的平移问题、二次函数与一元二次方程的联系等知识点,熟练掌握并灵活运用二次函数的图象与性质是解题关键.

16.如图,折叠矩形纸片 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,使点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 落在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 边的点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 处, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为折痕, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> .设 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的长为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,用含有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的式子表示四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的面积是________

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【解析】

【分析】

首先根据题意可以设DE=EM=x,在三角形AEM中用勾股定理进一步可以用t表示出x,再可以设CF=y,连接MF,所以BF=2y,在三角形MFN与三角形MFB中利用共用斜边,根据勾股定理可求出用t表示出y,进而根据四边形的面积公式可以求出答案.

【详解】设DE=EM=x

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

x= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

CF=y,连接FM

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

BF=2y

又∵FN= yNM=1

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

y= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的面积为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 1

故答案为: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> .

【点睛】本题主要考查了勾股定理的综合运用,熟练掌握技巧性就可得出答案.

三、解答题

17.计算: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【解析】

【分析】

根据同底数幂相乘、乘积的幂、幂的乘方、同底数幂相除运算法则逐步求解即可.

【详解】解:原式 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了整式的乘除中幂的运算法则,熟练掌握公式及其运算法则是解决此类题的关键.

18.如图,直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 分别与直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> .求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】证明见解析.

【解析】

【分析】

先根据角平分线的定义可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再根据平行线的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,从而可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,然后根据平行线的判定即可得证.

【详解】 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了平行线的判定与性质、角平分线的定义等知识点,熟记平行线的判定与性质是解题关键.

19.为改善民生;提高城市活力,某市有序推行“地摊经济”政策.某社区志愿者随机抽取该社区部分居民,按四个类别: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 表示“非常支持”, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 表示“支持”, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 表示“不关心”, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 表示“不支持”,调查他们对该政策态度的情况,将结果绘制成如下两幅不完整的统计图.根据图中提供的信息,解决下列问题:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

1)这次共抽取了________名居民进行调查统计,扇形统计图中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类所对应的扇形圆心角的大小是________

2)将条形统计图补充完整;

2)该社区共有2000名居民,估计该社区表示“支持”的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类居民大约有多少人?

【答案】160 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ;(2)图见解析;(3)该社区表示“支持”的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类居民大约有1200人.

【解析】

【分析】

1)根据C类的条形统计图和扇形统计图的信息可得出总共抽取的人数,再求出D类居民人数的占比,然后乘以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 即可得;

2)根据(1)的结论,先求出A类居民的人数,再补全条形统计图即可;

3)先求出表示“支持”的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类居民的占比,再乘以2000即可得.

【详解】(1)总共抽取的居民人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (名)

D类居民人数的占比为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类所对应的扇形圆心角的大小是 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

故答案为:60 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

2A类居民的人数为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (名)

补全条形统计图如下所示:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

3)表示“支持”的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类居民的占比为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (名)

答:该社区表示“支持”的 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 类居民大约有1200人.

【点睛】本题考查了条形统计图和扇形统计图的信息关联、画条形统计图等知识点,熟练掌握统计调查的相关知识是解题关键.

20. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的网格中建立如图的平面直角坐标系,四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的顶点坐标分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> .仅用无刻度的直尺在给定网格中按下列步骤完成画图,并回答问题:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

1)将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,画出对应线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

2)在线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 上画点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,使 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (保留画图过程的痕迹);

3)连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,画点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 关于直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的对称点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,并简要说明画法.

【答案】1)见解析;(2)见解析;(3)见解析

【解析】

【分析】

1)根据题意,将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 即可;

2)将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 顺时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是正方形,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> DB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> AB于点E,则E点为所求;

3)将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,过E点作线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为所求.

【详解】解:(1)如图示,线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 得到的;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

2)将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 顺时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

则四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是正方形,连接 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> DB <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> AB于点E

E点为所求,

理由如下:∵四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是正方形,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

则有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

E点为所求;

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

3)将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

E点作线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,交 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为所求;

理由如下:∵将线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 绕点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 逆时针旋转 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,

四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的顶点坐标分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是平行四边形,

根据 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是平行四边形 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的对角线,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 垂直平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 关于直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的对称点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了作图-旋转变换,正方形的性质,全等三角形的性质和轴对称的性质,熟悉相关性质是解题的关键.

21.如图,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为直径的⊙O <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 与过点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的切线互相垂直,垂足为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

1)求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

2)若 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值.

【答案】1)证明见解析;(2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【解析】

【分析】

1)如图(见解析),先根据圆的切线的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再根据平行线的判定与性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,然后根据等腰三角形的性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,最后根据角平分线的定义即可得证;

2)如图(见解析),先根据角的和差、等量代换可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再根据三角形全等的判定定理与性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,设 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,然后根据相似三角形的判定与性质可得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,从而可求出x的值,最后根据正弦三角函数的定义即可得.

【详解】(1)如图,连接OD

由圆的切线的性质得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 平分 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

2)如图,连接BD

由圆周角定理得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,且 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (不符题意,舍去)

经检验, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是所列分式方程的解

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

则在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了圆周角定理、圆的切线的性质、正弦三角函数、相似三角形的判定与性质等知识点,较难的是题(2),通过作辅助线,构造全等三角形和相似三角形是解题关键.

22.某公司分别在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城生产同种产品,共100件. <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 城生产品的总成本 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (万元)与产品数量 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> (件)之间具有函数关系 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 城生产产品的每件成本为70万元.

1)求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值;

2)当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城生产这批产品的总成本的和最少时,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城各生产多少件?

3)从 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 城把该产品运往 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两地的费用分别为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 万元/件和3万元/件;从 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 城把该产品运往 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两地的费用分别为1万元/件和2万元/件, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 地需要90件, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 地需要10件,在(2)的条件下,直接写出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和的最小值(用含有 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的式子表示).

【答案】1 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ;(2A城生产20件,B城生产80件;(3)当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和的最小值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 万元;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和的最小值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 万元.

【解析】

【分析】

1)先根据题意得出产品数量为0时,总成本y也为0,再利用待定系数法即可求出ab的值;

2)先根据(1)的结论得出yx的函数关系式,从而可得出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城生产这批产品的总成本的和,再根据二次函数的性质即可得;

3)设从A城运往C地的产品数量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 件, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,先列出从A城运往D地的产品数量、从B城运往C地的产品数量、从B城运往D地的产品数量,再求出n的取值范围,然后根据题干运费信息列出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的函数关系式,最后根据一次函数的性质求解即可得.

【详解】(1)由题意得:当产品数量为0时,总成本也为0,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

2)由(1)得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城生产这批产品的总成本的和为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

整理得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

由二次函数的性质可知,当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 取得最小值,最小值为6600万元

此时 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

答:A城生产20件,B城生产80件;

3)设从A城运往C地的产品数量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 件, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,则从A城运往D地的产品数量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 件,从B城运往C地的产品数量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 件,从B城运往D地的产品数量为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

由题意得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,解得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

整理得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

根据一次函数的性质分以下两种情况:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 内, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的增大而减小

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 取得最小值,最小值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时,在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 内, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的增大而增大

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 取得最小值,最小值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

答:当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和的最小值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 万元;当 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 时, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两城总运费的和的最小值为 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 万元.

【点睛】本题考查了利用待定系数法求二次函数的解析式、二次函数与一次函数的实际应用等知识点,较难的是题(3),正确设立未知数,建立函数关系式是解题关键.

23.问题背景:如图(1),已知 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,求证: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

尝试应用:如图(2),在 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 中, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 相交于点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> .点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 边上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,求 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的值;

拓展创新:如图(3), <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 内一点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,直接写出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的长.

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【答案】问题背景:见详解;尝试应用:3;拓展创新: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【解析】

【分析】

问题背景:通过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再找到相等的角,从而可证 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

尝试应用:连接CE,通过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 可以证得 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,得到 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,然后去证 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,通过对应边成比例即可得到答案;

拓展创新:在AD的右侧作∠DAE=∠BACAEBD延长线于E,连接CE,通过 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,然后利用对应边成比例即可得到答案.

【详解】问题背景:∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

∴∠BAC=∠DAE <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

∴∠BAD+∠DAC=CAE+∠DAC

∴∠BAD=∠CAE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

尝试应用:连接CE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

∵∠BAD+∠DAC=CAE+∠DAC

∴∠BAD=∠CAE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

由于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,即 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

又∵ <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

拓展创新: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

如图,在AD的右侧作∠DAE=∠BACAEBD延长线于E,连接CE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

∵∠ADE=∠BAD+∠ABD,∠ABC=∠ABD+∠CBD <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

∴∠ADE=∠ABC

又∵∠DAE=∠BAC

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

又∵∠DAE=∠BAC

∴∠BAD=∠CAE

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

CD=x,在直角三角形BCD中,由于∠CBD=30°

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

【点睛】本题考查了相似三角形的综合问题,熟练掌握相似三角形的判定和性质是解题的关键.

24.将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向下平移6个单位长度得到抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向左平移2个单位长度得到抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

1)直接写出抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的解析式;

2)如图(1),点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 对称轴 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 右侧上,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在对称轴 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 上, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是以 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为斜边的等腰直角三角形,求点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的坐标;

3)如图(2),直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为常数)与抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的中点;直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 与抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两点, <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为线段 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的中点.求证:直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 经过一个定点.

【答案】1)抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的解析式为: y=x2-4x-2;抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的解析式为:y=x2-6;(2)点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的坐标为(53)或(4-2);(3)直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 经过定点(02

【解析】

【分析】

1)根据函数图象上下平移:函数值上加下减;左右平移:自变量左加右减写出函数解析式并化简即可;

2)先判断出点ABOD四点共圆,再根据同弧所对的圆周角相等得到∠BDA=∠BOA=45°,从而证出 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是等腰直角三角形.设点A的坐标为(xx2-4x-2),把DCAC用含x的代数式表示出来,利用DC=AC列方程求解即可,注意有两种情况;

3)根据直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为常数)与抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两点,联立两个解析式,得到关于x的一元二次方程,根据根与系数的关系求出点M的横坐标,进而求出纵坐标,同理求出点N的坐标,再用待定系数法求出直线MN的解析式,从而判断直线MN经过的定点即可.

【详解】解:(1)∵抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向下平移6个单位长度得到抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ,再将抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 向左平移2个单位长度得到抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的解析式为:y=(x-2)2-6,即y=x2-4x-2

抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的解析式为:y=(x-2+2)2-6,即y=x2-6

2)如下图,过点AAC⊥x轴于点C,连接AD

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是等腰直角三角形,

∴∠BOA =45°

又∵∠BDO=∠BAO=90°

ABOD四点共圆,

∴∠BDA=∠BOA=45°

∴∠ADC=90°-∠BDA=45°

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 是等腰直角三角形,

DC=AC

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 对称轴 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 右侧上,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 在对称轴 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 上,

抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的对称轴为x=2

设点A的坐标为(xx2-4x-2),

DC=x-2AC= x2-4x-2

x-2= x2-4x-2

解得:x=5x=0(舍去),

A的坐标为(53);

同理,当点B、点Ax轴的下方时,

x-2= -(x2-4x-2)

x=4x=-1(舍去),

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的坐标为(4-2),

综上,点 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 的坐标为(53)或(4-2).

3)∵直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 为常数)与抛物线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 交于 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 两点,

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

x2-kx-6=0

设点E <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 横坐标为xE,点F的横坐标为xF

xE+xF=k

中点M的横坐标xM= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> = <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

中点M的纵坐标yM=kx= <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

M的坐标为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> );

同理可得:点N的坐标为( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ),

设直线MN的解析式为y=ax+ba≠0),

M <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> )、N <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> )代入得:

 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

解得: <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a>

直线MN的解析式为y=  <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ·x+2 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ),

不论k取何值时( <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> ),当x=0时,y=2

直线 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 经过定点(02).

【点睛】本题考查二次函数综合应用,熟练掌握图象平移 <a href="/tags/51/" title="试题" class="c1" target="_blank">试题</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/203/" title="武汉" class="c1" target="_blank">武汉</a> <a href="/tags/557/" title="湖北" class="c1" target="_blank">湖北</a> <a href="/tags/975/" title="湖北省" class="c1" target="_blank">湖北省</a> 规律、判断点ABOD四点共圆的方法、用待定系数法求函数解析式的步骤是解题的关键.