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(1)2;(2)(
![](https://img.yulucn.com/upload/a/eb/aebf6ba0e20ec7b5a9996aaf4ddc4f1b_thumb.jpg)
,8)或(
![](https://img.yulucn.com/upload/8/79/8791565e0ef07a76d7f997996d014247_thumb.jpg)
,8)或(
![](https://img.yulucn.com/upload/4/9f/49f697b0b48f200020ae31ca07e5f137_thumb.jpg)
,4)或(
![](https://img.yulucn.com/upload/a/6c/a6c1dae0d8059d3795792077e81a4e1e_thumb.jpg)
,4);(3)2m-2或
试题分析:(1)在二次函数的解析式
![](https://img.yulucn.com/upload/5/7d/57de9688c7f063e36dbb5ca09b44ab1b_thumb.jpg)
中,令y=0,求出x=±1,得到AB=2,令x=0时,求出y=-2,得到OC=2,然后根据三角形的面积公式即可求出△ABC的面积;
(2)先将y=6代入
![](https://img.yulucn.com/upload/5/7d/57de9688c7f063e36dbb5ca09b44ab1b_thumb.jpg)
,求出x=±2,得到点M与点N的坐标,则MN=4,再由平行四边形的面积公式得到MN边上的高为2,则P点纵坐标为8或4.分两种情况讨论:①当P点纵坐标为8时,将y=8代入
![](https://img.yulucn.com/upload/5/7d/57de9688c7f063e36dbb5ca09b44ab1b_thumb.jpg)
,求出x的值,得到点P的坐标;②当P点纵坐标为4时,将y=4代入
![](https://img.yulucn.com/upload/5/7d/57de9688c7f063e36dbb5ca09b44ab1b_thumb.jpg)
,求出x的值,得到点P的坐标;
(3)由于∠QDB=∠BOC=90°,所以以Q,D,B为顶点的三角形和以B,C,O为顶点的三角形相似时,分两种情况讨论:①OB与BD边是对应边,②OB与QD边是对应边两种情况,根据相似三角形对应边成比例列式计算求出QD的长度即可.
试题解析:(1)∵
![](https://img.yulucn.com/upload/5/7d/57de9688c7f063e36dbb5ca09b44ab1b_thumb.jpg)
,
∴当y=0时,2x2-2=0,x=±1,
∴点A的坐标为(-1,0),点B的坐标为(1,0),AB=2,
又当x=0时,y=-2,
∴点C的坐标为(0,-2),OC=2,
∴
![](https://img.yulucn.com/upload/f/ab/fab58385868b77c56e829800a5cf6aa2_thumb.jpg)
AB•OC
![](https://img.yulucn.com/upload/b/76/b768062b8ddda7cfabd91c690d01dfd3_thumb.jpg)
×2×2=2;
(2)将y=6代入
![](https://img.yulucn.com/upload/5/7d/57de9688c7f063e36dbb5ca09b44ab1b_thumb.jpg)
,
得
![](https://img.yulucn.com/upload/1/47/147c8c0416808e74739e63ea729f7c87_thumb.jpg)
,解得x=±2,
∴点M的坐标为(-2,6),点N的坐标为(2,6),MN=4.
∵平行四边形的面积为8,
∴MN边上的高为:8÷4=2,
∴P点纵坐标为6±2.
①当P点纵坐标为6+2=8时,
![](https://img.yulucn.com/upload/3/24/3241e4028bbf3ee3b31b613c10e631b8_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/4/d8/4d801f0001a79ba5bf7527a01acc8bd1_thumb.jpg)
,
∴点P的坐标为(
![](https://img.yulucn.com/upload/a/eb/aebf6ba0e20ec7b5a9996aaf4ddc4f1b_thumb.jpg)
,8)或(
![](https://img.yulucn.com/upload/8/79/8791565e0ef07a76d7f997996d014247_thumb.jpg)
,8);
②当P点纵坐标为6-2=4时,
![](https://img.yulucn.com/upload/b/b2/bb2c715dd5a4050fce483cc40c985f51_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/9/6d/96de1420ecfc59326d9d066ad687ea36_thumb.jpg)
,
∴点P的坐标为(
![](https://img.yulucn.com/upload/4/9f/49f697b0b48f200020ae31ca07e5f137_thumb.jpg)
,4)或(
![](https://img.yulucn.com/upload/e/7a/e7a5445770c6fdc48095e74033949ed5_thumb.jpg)
,4);
(3)∵点B的坐标为(1,0),点C的坐标为(0,-2),
∴OB=1,OC=2.
∵∠QDB=∠BOC=90°,
∴以Q,D,B为顶点的三角形和以B,C,O为顶点的三角形相似时,分两种情况:
①OB与BD边是对应边时,△OBC∽△DBQ,
则
![](https://img.yulucn.com/upload/d/f5/df554871cde71266096e63fc547ee7e9_thumb.jpg)
,即
![](https://img.yulucn.com/upload/d/55/d551753a7153654bbc2473062e9b93e7_thumb.jpg)
,解得DQ=2(m-1)=2m-2,
②OB与QD边是对应边时,△OBC∽△DQB,
则
![](https://img.yulucn.com/upload/2/6f/26fc93daf4877326666c74cd2ac70534_thumb.jpg)
,即
![](https://img.yulucn.com/upload/6/24/6246a2ba7a1563f360cb999406ab15f7_thumb.jpg)
,解得
![](https://img.yulucn.com/upload/a/a9/aa96eace7369b712e583a62c9c375053_thumb.jpg)
.
综上所述,线段QD的长为2m-2或
![](https://img.yulucn.com/upload/5/07/5071f58421d76b721faed0c7c44c4191_thumb.jpg)
.
1年前
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