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

Step2: Analyze the transformation visually

Observing the positions of Figure A and Figure B, if we take a general point $(x,y)$ on Figure A and consider a counter - clockwise rotation of 180 degrees about the origin, we get $(-x,-y)$. This transformation maps Figure A to Figure B.

Answer:

A counterclockwise rotation of 180 about the origin