配套习题- 二次函数压轴题——直角三角形问题 -【青果学院】

1/5单选题

难度：

1.如图，在平面直角坐标系中，△ABC是直角三角形，∠ACB=90，AC=BC，OA=1，OC=4，抛物线y=x²-2x-3经过A，B两点，抛物线的顶点为D. 点E是直角三角形ABC斜边AB上一动点（点A、B除外），过点E作x轴的垂线交抛物线于点F，当线段EF的长度最大时，点E的坐标为（）

A
B
C
D

正确答案：QQ==

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

2/5单选题

难度：

2.二次函数y=x²-2x-1的图象与x轴交于A，B两点，与y轴交于点P，顶点为C（1，-2）. 作点C关于x轴的对称点D，顺次连接A，C，B，D. 若抛物线上一点E（3，2），直线PE恰好把四边形ABCD分成面积相等的两个四边形，抛物线上一点F，使得△PEF是以P为直角顶点的直角三角形，则F的坐标为（）

A	（1，-2）
B	（2，-1）
C	（-1，2）
D	（-2，-2）

正确答案：QQ==

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

3/5单选题

难度：

3.如图，在矩形OABC中，点O为原点，点A的坐标为（0，8），点C的坐标为（6，0）. 抛物线y=-

x²+bx+c经过点A、C，与AB交于点D. 点P为线段BC上一个动点（不与点C重合），点Q为线段AC上一个动点，AQ=CP，连接PQ，设CP=m，△CPQ的面积为S. 当S最大时，在抛物线y=-

x²+bx+c的对称轴l上，使△DFQ为直角三角形的点F有（）个

A	1
B	2
C	3
D	4

正确答案：RA==

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

4/5单选题

难度：

4.如图，四边形OABC为直角梯形，A（4，0），B（3，4），C（0，4）. 点M从O出发以每秒2个单位长度的速度向A运动；点N从B同时出发，以每秒1个单位长度的速度向C运动. 其中一个动点到达终点时，另一个动点也随之停止运动. 过点N作NP垂直x轴于点P，连接AC交NP于Q，连接MQ. 则使得△AQM为直角三角形的点M的坐标为（）

A	（1，0）或（3，0）
B	（2，0）或（4，0）
C	（1，0）或（2，0）
D	（3，0）或（4，0）

正确答案：Qw==

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

5/5单选题

难度：

5.如图所示，矩形OABC位于平面直角坐标系中，AB=2，OA=3，点P是OA上的任意一点，PB平分∠APD，PE平分∠OPF，且PD、PF重合. 当PD⊥OA时，经过E、P、B三点的抛物线的解析式为y=

x²-

x+1，抛物线上使得△EPM为直角三角形的M点的坐标为（）

A	（3，2），（4，5）
B	（1，2），（4，5）
C	（3，2），（3，5）
D	（1，2），（3，5）

正确答案：QQ==

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