Question

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

Explanation:

Step1: Recall rotation and reflection rules

For a point $(x,y)$ rotated 180 - degrees counter - clockwise about the origin, the new point is $(-x,-y)$. For a 90 - degree counter - clockwise rotation about the origin, the new point is $(-y,x)$. For a reflection over $y = x$, the new point is $(y,x)$ and for a reflection over $y=-x$, the new point is $(-y,-x)$.

Step2: Analyze the transformation from figure A to figure B

If we take a general point $(x,y)$ on figure A and observe its corresponding point on figure B, we can see that if the point on figure A is $(x,y)$, the point on figure B is $(-x,-y)$. This is the rule for a 180 - degree counter - clockwise rotation about the origin.

Answer:

A counterclockwise rotation of 180° about the origin