2019 AMC 12B 第 3 题

Question

下列哪个刚性变换（等距变换）把线段

\overline{AB}

映到线段

\overline{A'B'}

，使得

A(-2,1)

的像是

A'(2,-1)

，且

B(-1,4)

的像是

B'(1,-4)

？

Which one of the following rigid transformations (isometries) maps the line segment

\overline{AB}

onto the line segment

\overline{A'B'}

so that the image of

A(-2,1)

is

A'(2,-1)

and the image of

B(-1,4)

is

B'(1,-4)?

关于

y

-轴反射

reflection in the

y

-axis

绕原点逆时针旋转

90^\circ

counterclockwise rotation around the origin by

90^\circ

向右平移

3

个单位并向下平移

5

个单位

translation by

3

units to the right and

5

units down

关于

x

-轴反射

reflection in the

x

-axis

绕原点顺时针旋转

180^\circ

clockwise rotation about the origin by

180^\circ

答案：E

知识点：变换坐标几何

难度评级：1080

小提示：

追踪坐标变化：

(-2,1)\to(2,-1)

且

(-1,4)\to(1,-4)

Track the coordinate change:

(-2,1)\to(2,-1)

and

(-1,4)\to(1,-4)

大提示：

两个点都遵循规则

(x,y)\to(-x,-y)

Both points follow the rule

(x,y)\to(-x,-y)

解答：

每个点都按

(x,y)\to(-x,-y)

映射：确实有

(-2,1)\to(2,-1)

且

(-1,4)\to(1,-4)

。

映射

(x,y)\to(-x,-y)

是绕原点旋转

180^\circ

。

所以正确答案是 E。

Each point maps by

(x,y)\to(-x,-y):

indeed

(-2,1)\to(2,-1)

and

(-1,4)\to(1,-4).

The map

(x,y)\to(-x,-y)

is a

180^\circ

rotation about the origin.

Thus, E is the correct answer.

2019 AMC 12B 第 3 题

答案：E

难度评级：1080

小提示：

大提示：

解答：

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