Question

which transformation would take figure a to figure b? answer a clockwise rotation of 180 about the origin a clockwise 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 - degree clock - wise about the origin, the new point is $(-x,-y)$. For a 90 - degree clock - wise rotation about the origin, the new point is $(y, - x)$. For reflection over $y=-x$, the point $(x,y)$ becomes $(-y,-x)$ and for reflection over $y = x$, the point $(x,y)$ becomes $(y,x)$.

Step2: Analyze the transformation visually

By observing the positions of Figure A and Figure B, we can see that if we take a general point $(x,y)$ on Figure A and rotate it 180 degrees clock - wise about the origin to get $(-x,-y)$, it will match the corresponding point on Figure B.

Answer:

A clockwise rotation of 180 about the origin