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【324310】2024八年级数学下册 专题突破 期末复习6 四边形期末复习之存在性问题专题复习(含解

时间:2025-01-15 21:56:28 作者: 字数:15849字
简介:


 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 期末复习6 四边形期末复习之存在性问题专题复习

1.(东阳市期末)如图,四边形OBAC是矩形,OC2OB6,反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 的图象过点A

1)求k的值.

2)点P为反比例图象上的一点,作PD直线ACPEx轴,当四边形PDCE是正方形时,求点P的坐标.

3)点G为坐标平面上的一点,在反比例函数的图象上是否存在一点Q,使得以ABQG为顶点组成的平行四边形面积为14?若存在,请求出点G的坐标;若不存在,请说明理由.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

【分析】(1)先求出点A坐标,代入解析式可求解;

2)分两种情况讨论,由正方形的性质可求解;

3)由平行四边形的面积为14,可求点Q坐标,再分AB为边和对角线两种情况讨论,由平行四边形的性质和中点坐标公式可求解.

【解答】解:(1)∵OC2OB6

C20),点B06),点A26),

反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 的图象过点A

k2×612

2)∵k12

反比例函数解析式为:y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

设点Pa <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

四边形PDCE是正方形,

PDPE

当点P在第一象限时,

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> a﹣2

a1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +1a21﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> (舍去)

P <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 1);

当点P在第三象限,

∴﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2﹣a

a1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +1(舍去),a21﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

P1﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,﹣1﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> );

综上所述:点P坐标为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 1)或(1﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,﹣1﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> );

3)设点Q坐标为(b <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

AB为边,

ABQG为顶点组成的平行四边形面积为14

2×|6﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> |14

b1=﹣12b2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

Q(﹣12,﹣1)或( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 13),

ABQG为顶点组成的四边形是平行四边形,

ABQG2ABQG

G(﹣10,﹣1)或(﹣14,﹣1)或( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 13)或(﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 13);

AB为对角线,

设点Gxy),

ABQG为顶点组成的四边形是平行四边形,

ABQG互相平分,

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

x114y113,或x2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> y2=﹣1

G1413)或( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,﹣1),

综上所述:点G的坐标为(﹣10,﹣1)或(﹣14,﹣1)或( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 13)或(﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 13)或(1413)或( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,﹣1).

2.(丽水期中)如图,在菱形ABCD中,∠DAB60°AB2,点EAB边上的动点,作∠EDQ60°BC于点Q,点PAD上,PDPE

1)求证:AEBQ

2)连接PQEQ,当∠PEQ90°时,求 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 的值;

3)当AE为何值时,△PEQ是等腰三角形.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

【分析】(1)如图1中,连接BD.证明△ADE≌△BDQSAS)即可.

2)如图2中,连接EQPQBD.首先证明△DEQ是等边三角形,求出DE,证明四边形APQB是平行四边形即可.

3)分两种情形:如图3﹣1中,当QPQE时,作QMCDM.求出CQ即可.如图3﹣2中,当PEQE时,点EB重合,点PA重合,点QC重合,此时AEAB2

【解答】(1)证明:如图1中,连接BD

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

四边形ABCD是菱形,

∴∠A=∠C60°ABBCBDCD

∴△ABD,△BDC都是等边三角形,

∴∠A=∠DBQ60°ADDB

∵∠ADB=∠EDQ60°

∴∠ADE=∠BDQ

∴△ADE≌△BDQASA),

AEBQ


2)解:如图2中,连接EQPQBD

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∵△ADE≌△BDQ

DEDQ

∵∠EDQ60°

∴△DEQ是等边三角形,

DEDQEQ,∠DEQ60°

∵∠PEQ90°

∴∠PED30°

PDPE

∴∠PDE=∠EPD30°

∵∠A60°

∴∠AED90°

DEAB,∵AB2

AEEB1

DE <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

PDPEQDQE

PQDE

PQAB,∵ADBC

四边形PQBA是平行四边形,

PQAB2

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


3)解:如图3﹣1中,当QPQE时,作QMCDM

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

QDQEQPQP垂直平分线段DE

∴∠DQP=∠EQP30°

∴∠ADQ75°

∵∠ADC120°

∴∠QDM45°,设CMa,则CQ2aDMQM <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> a

CDAB2

a+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> a2

a <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 1

CQ2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ﹣2

AEBQBCCQ4﹣2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


如图3﹣2中,当PEQE时,点EB重合,点PA重合,点QC重合,此时AEAB2

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

综上所述,满足条件的AE的值为4﹣2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2


3.(湖州)如图1,在平面直角坐标系xOy中,已知△ABC,∠ABC90°,顶点A在第一象限,BCx轴的正半轴上(CB的右侧),BC2AB2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,△ADC与△ABC关于AC所在的直线对称.

1)当OB2时,求点D的坐标;

2)若点A和点D在同一个反比例函数的图象上,求OB的长;

3)如图2,将(2)中的四边形ABCD向右平移,记平移后的四边形为A1B1C1D1,过点D1的反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> k≠0)的图象与BA的延长线交于点P.问:在平移过程中,是否存在这样的k,使得以点PA1D为顶点的三角形是直角三角形?若存在,请直接写出所有符合题意的k的值;若不存在,请说明理由.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

【分析】(1)如图1中,作DEx轴于E,解直角三角形清楚DECE即可解决问题;

2)设OBa,则点A的坐标(a2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),由题意CE1DE <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,可得D3+a <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),点AD在同一反比例函数图象上,可得2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> a <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 3+a),清楚a即可;

3)分两种情形:①如图2中,当点A1在线段CD的延长线上,且PA1AD时,∠PA1D90°

如图2中,利用勾股定理的逆定理,构建方程分别求解;

【解答】解:(1)如图1中,作DEx轴于E

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

∵∠ABC90°

tan∠ACB <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

∴∠ACB60°

根据对称性可知:DCBC2,∠ACD=∠ACB60°

∴∠DCE60°

∴∠CDE90°﹣60°30°

CE1DE <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

OEOB+BC+CE5

D坐标为(5 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ).


2)设OBa,则点A的坐标(a2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

由题意CE1DE <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,可得D3+a <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

AD在同一反比例函数图象上,

2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> a <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 3+a),

a3

OB3


3)存在.理由如下:

如图2中,当点A1在线段CD的延长线上,且PA1AD时,∠PA1D90°

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

Rt△ADA1中,∵∠DAA130°AD2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

AA1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 4

Rt△APA1中,∵∠APA160°

PA <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

PB <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

由(2)可知P3 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

k10 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


如图2中,由题意D6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),设P3 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),A13+h2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),D16+h <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

PD232+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2DA12=(3﹣h2+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2PA12h2+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2

当∠PA1D90°时,32+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2=(3﹣h2+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2+h2+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 2

又∵ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 6+h)=3

可得k10 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

当∠PDA190°时,同法可得k12 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

综上所述,k的值为10 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 12 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

4.(永康市期末)如图,在平面直角坐标系中,平行四边形OABC的顶点Ax轴上,BC在第一象限,反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> k≠0)的图象经过点C,交ABD,已知OC12OA4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,∠AOC60°

1)求反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> k≠0)的函数表达式;

2)连接CD,求△BCD的面积;

3P是线段OC上的一个动点,以AP为一边,在AP的右上方作正方形APEF,在点P的运动过程中,是否存在一点P使顶点E落在▱OABC的边所在的直线上,若存在,请求出此时OP的长,若不存在,请说明理由.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

【分析】(1)过点CCGx轴于点G,构造含60°角的Rt△OCG,利用OC12和∠AOC的正弦余弦值,即求得OGCG的长,得到点C坐标,用待定系数法即求得反比例函数表达式.

2)由平行四边形OABC边长OA4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 可求得点B坐标,进而求直线AB解析式.把直线AB解析式和反比例函数解析式联立方程组,求解即得到点D坐标.过点DDHBC于点H,易得SBCD <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> BCDH,代入计算即求得△BCD的面积.

3)求直线OC解析式,设点P横坐标为m,用m表示其纵坐标.过点PPMx轴于点M,过点EEN直线PM于点N,由正方形APEF性质即可证△PNE≌△AMP,可得PNAM4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> NEPM,即得到用m表示点E坐标.由于点E可能落在▱OABC的边OCBCAB上,故需分类讨论.①落在OC上时,把点E坐标代入直线OC解析式,解方程求m即得到点P坐标,进而求OP的长;②落在BC上,则点E纵坐标等于点C纵坐标,列得方程;③落在AB上,把点E坐标代入直线AB解析式再解方程.

【解答】解:(1)如图1,过点CCGx轴于点G

∴∠OGC90°

OC12,∠AOC60°

cos∠AOC <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> sin∠AOC <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

OG <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> OC6CG <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> OC6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

C66 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> k≠0)的图象经过点C

6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 解得:k36 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

反比例函数的函数表达式为y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


2)如图2,过点DDHBC于点H

OA4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,点Ax轴上

A4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 0

四边形OABC是平行四边形

BCOABCOA4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

xBxC+BC6+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> yByHyC6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

B6+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

设直线AB解析式为yax+b

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 解得: <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

直线ABy <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x﹣12

D为线段AB与反比例函数图象的交点

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 解得: <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> (舍去)

D6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 6

DH6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ﹣6

SBCD <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> BCDH <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ×4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ×6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ﹣6)=36﹣12 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


3)存在点P使顶点E落在▱OABC的边所在的直线上.

如图3,过点PPMx轴于点M,过点EEN直线PM于点N

∴∠AMP=∠PNE90°

C66 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

直线OC解析式为y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x

P在线段OC

设点P坐标为(m <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m)(0≤m≤6

OMmPM <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

AMOAOM4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

四边形APEF是正方形

APPE,∠APE90°

∴∠EPN+∠APM=∠APM+∠PAM90°

∴∠EPN=∠PAM

在△PNE与△AMP

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

∴△PNE≌△AMPAAS

PNAM4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> mNEPM <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

xExN+NEm+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> myEyNMNPM+PN <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

Em+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

若点E落在直线OC上,则 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

解得:m <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

P <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 3),OP <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

若点E落在直线BC上,则 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m6 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

解得:m3+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

P3+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 3 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +3),OP <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

若点E落在直线AB上时,直线ABy <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x﹣12

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m)﹣12 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m+4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m

解得:m3+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,即点E落在直线BC与直线AB交点处

综上所述,OP2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 或(6+2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> )时,点E落在▱OABC的边所在的直线上.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


5.(杭州期末)如图,四边形ABCD的四个顶点分别在反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x00mn)的图象上,对角线BDy轴,且BDAC于点P.已知点B的横坐标为4

1)当m4n20时.

若点P的纵坐标为2,求点A和点B的坐标.

若点PBD的中点,试判断四边形ABCD的形状,并说明理由.

2)四边形ABCD能否成为正方形?若能,求此时mn之间的数量关系;若不能,试说明理由.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

【分析】(1)①利用反比例函数图象上点的坐标特征,可得出点AB的坐标;

由①可得出点BD,由点P为线段BD的中点可得出点P的坐标,利用反比例函数图象上点的坐标特征可得出点AC的坐标,进而可得出PAPC,结合PBPD可得出四边形ABCD为平行四边形,再结合BDAC可得出四边形ABCD为菱形;

2)当四边形ABCD为正方形时,设PAPBPCPDtt≠0),利用反比例函数图象上点的坐标特征可得出点B的坐标,由PAPBt可得出点A的坐标,利用反比例函数图象上点的坐标特征可得出t4﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,由点B的坐标结合BD2t可得出点D的坐标,再利用反比例函数图象上点的坐标特征可得出m+n32

【解答】解:(1)①当x4时,y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 1

B的坐标为(41);

y2时,2 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,解得:x2

A的坐标为(22).

四边形ABCD为菱形,理由如下:

由①得:点B的坐标为(41),点D的坐标为(45),

P为线段BD的中点,

P的坐标为(43).

y3时,3 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,解得:x <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

A的坐标为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 3);

y3时,3 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,解得:x <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

C的坐标为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 3).

PA4﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> PC <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

PAPC

PBPD

四边形ABCD为平行四边形.

又∵BDAC

四边形ABCD为菱形.

2)四边形ABCD能成为正方形.

当四边形ABCD为正方形时,设PAPBPCPDtt≠0).

x4时,y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

B的坐标为(4 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

A的坐标为(4﹣t <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +t).

A在反比例函数y <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> 的图象上,

4﹣t)( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +t)=m,化简得:t4﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

D的纵坐标为 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +2t <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> +24﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> )=8﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

D的坐标为(48﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

8﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> )=n,整理,得:m+n32

即四边形ABCD能成为正方形,此时m+n32

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


6.(宁波期末)【基础巩固】

1)如图1ACDFRt△ABC≌Rt△DEF,连结ADBE,求证:四边形ABED是平行四边形.

【尝试应用】

2)如图2,在平面直角坐标系xOy中,已知点AB的坐标分别是A13),B41),点Cx轴上,点Dy轴上.若以AB为边,其余两个顶点为CD的四边形是平行四边形,求点CD的坐标.

【拓展提高】

3)如图3,抛物线yx2﹣4x+3与直线yx+3交于CD两点,点E是抛物线上任意一点,在对称轴上是否存在点F,使得以CD为边,其余两个顶点为EF的四边形是平行四边形,若存在,求出点E的坐标,若不存在,请说明理由.

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

【分析】(1)连接CF,先证四边形ADFC是平行四边形,再推导出∠BAD+∠ADE180°,则有ABDE,即可证明;

2)求出AB <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,再求直线AB的解析式为y=﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,由于CDABCDAB,设CD的直线解析式为y=﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x+m,可求D0m),C <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m0),则CD <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> |m| <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,求出m±2,即可求点的坐标;

3)先求出C58),D03),设F2n),Ett2﹣4t+3),由已知可分两种情况①当DFCE为对角线时,DF的中点为(1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),CE的中点为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),则1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,求出t=﹣3,即可求E(﹣324);②当DECF为对角线时,DE的中点为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),CF的中点为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),则 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ,求出t7,即可求E724).

【解答】解:(1)连接CF

Rt△ABC≌Rt△DEF

ACDFABDE

ACDF

四边形ADFC是平行四边形,

∴∠CAD+∠ADF180°

∵∠BAC=∠EDF

∴∠BAD+∠ADE180°

ABDE

四边形ADEB是平行四边形;

2)∵A13),B41),

AB <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

AB的直线解析式为ykx+b

则有 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

直线AB的解析式为y=﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x+ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

四边形是以AB为边,

CDABCDAB

CD的直线解析式为y=﹣ <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> x+m

D点在y轴上,C点在x轴上,

D0m),C <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> m0),

CD <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> |m|

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> |m| <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

m±2

D02),C30)或D0,﹣2),C(﹣30);

3)存在,理由如下:

抛物线yx2﹣4x+3与直线yx+3交于CD两点,

x2﹣4x+3x+3

解得x0x5

C58),D03),

抛物线对称轴为直线x2

F2n),Ett2﹣4t+3),

平行四边形是以CD为边,

DFCE为对角线时,

DF的中点为(1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),CE的中点为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

1 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

t=﹣3

E(﹣324);

DECF为对角线时,

DE的中点为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),CF的中点为( <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a> ),

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>  <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>

t7

E724);

综上所述:满足条件的E点坐标为(﹣324)或(724).

 <a href="/tags/14/" title="复习" class="c1" target="_blank">复习</a> <a href="/tags/38/" title="突破" class="c1" target="_blank">突破</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/129/" title="四边形" class="c1" target="_blank">四边形</a> <a href="/tags/282/" title="专题" class="c1" target="_blank">专题</a>


1