Question

which transformation would take figure a to figure b? answer a counterclockwise rotation of 90° about the origin a reflection over the line y = -x a counterclockwise rotation of 180° about the origin a reflection over the line y = x

Explanation:

Step1: Recall rotation and reflection rules

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

Step2: Analyze the transformation visually

Observe the orientation and position of Figure A and Figure B. The transformation from Figure A to Figure B is a counter - clockwise rotation of 90° about the origin. For example, if we consider a vertex of Figure A at $(x,y)$ and its corresponding vertex in Figure B, it follows the rule of a 90° counter - clockwise rotation about the origin.

Answer:

A. A counterclockwise rotation of 90° about the origin