AMC12 2022 B

AMC12 2022 B · Q5

AMC12 2022 B · Q5. It mainly tests Transformations.

The point $(-1, -2)$ is rotated $270^{\circ}$ counterclockwise about the point $(3, 1)$. What are the coordinates of its new position?

点 $(-1, -2)$ 绕点 $(3, 1)$ 逆时针旋转 $270^{\circ}$。其新位置的坐标是多少？

(A) \ (-3, -4) \ (-3, -4)

(B) \ (0,5) \ (0,5)

(D) \ (4,3) \ (4,3)

(E) \ (6,-3) \ (6,-3)

Answer

Correct choice: (B)

正确答案：（B）

Solution

$(-1,-2)$ is $4$ units west and $3$ units south of $(3,1)$. Performing a counterclockwise rotation of $270^{\circ}$, which is equivalent to a clockwise rotation of $90^{\circ}$, the answer is $3$ units west and $4$ units north of $(3,1)$, or $\boxed{\textbf{(B)}\ (0,5)}$.

$(-1,-2)$ 是 $(3,1)$ 西 $4$ 单位、南 $3$ 单位。进行逆时针 $270^{\circ}$ 旋转，等价于顺时针 $90^{\circ}$ 旋转，结果是 $(3,1)$ 西 $3$ 单位、北 $4$ 单位，即 $\boxed{\textbf{(B)}\ (0,5)}$。

Topics

GE.011 Transformations