Question

answer attempt 1 out of 3 a reflection over the line y = -x a counterclockwise rotation of 180° about the origin a counterclockwise rotation of 90° about the origin a reflection over the line y = x

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ reflected over $y = -x$, the new - point is $(-y,-x)$. For a $180^{\circ}$ counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-x,-y)$. For a $90^{\circ}$ counter - clockwise rotation about the origin, the rule for a point $(x,y)$ is $(-y,x)$. For a reflection over $y = x$, the rule for a point $(x,y)$ is $(y,x)$.

Step2: Analyze the transformation from A to B

Let's take a general point $(x,y)$ on figure A. If we consider a $180^{\circ}$ counter - clockwise rotation about the origin, applying the rule $(x,y)\to(-x,-y)$ will map points from figure A to figure B.

Answer:

A counterclockwise rotation of 180° about the origin