配套习题- 二次函数压轴题——动点路径问题（二） -【青果学院】

1/5单选题

难度：

1.如图，在平面直角坐标系中，二次函数y=

图像与x轴交于B、C两点，与y轴交于A点，将△ABC绕点C逆时针旋转90°得到△A₂B₂C₂，直接写出点A运动到点A1时所经过的路径长正确的是（）.

A
B
C
D

正确答案：Qg==

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

2/5单选题

难度：

2.在直角坐标系中，抛物线

与x轴交于A（-8，0），以OA为边的正方形AOCD的中心恰好是抛物线的顶点E，如图所示，现将正方形AOCD按如图方式向右倾斜至边AD与对角线AC重合，此时，点C、D、E的对应点分别为点C′、D′、E′，那么点E所走过的路径的长为（ ).

A	4
B	4
C
D

正确答案：Qw==

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

3/5单选题

难度：

3.如图，在平面直角坐标系xOy中，二次函数

的图像与y轴交于点A（0，2），直线OP位于一、三象限，∠AOP=45°，设点A关于直线OP的对称点为B. 直线OP顺时针旋转n°（0＜n≤90），在这个运动过程中，点A关于直线OP的对称点所经过的路径长为（）

A
B
C
D

正确答案：RA==

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

4/5单选题

难度：

4.如图，直角坐标系xOy中，二次函数

的顶点为D，且与x轴交于AB两点，连接AD，以AD为半径作⊙D，交y轴负半轴点C，点E为⊙O上一动点，CF⊥AE于点F. 当点E从点B出发顺时针运动到点C时，点F所经过的路径长为（　　）

A
B
C
D

正确答案：Qw==

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

5/5单选题

难度：

5.二次函数

的图像与x轴交于C、D两点，以CD为直径的⊙O交y轴于A、B点，如图所示，AB、CD是互相垂直的两条直径，点P是⊙O任意一点，过点P作PM⊥AB于M，PN⊥CD于N，点Q是MN的中点，当点P沿着圆圈走过45°弧长时，点Q走过的路径长为（　　）

A
B
C
D

正确答案：QQ==

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