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

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

解答：

其他年份的第 3 题