Question

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

Explanation:

Step1: Recall transformation rules

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

Step2: Analyze the orientation of the figures

Let's assume a general point $(x,y)$ on Figure A. If we consider a counter - clockwise rotation of $180^{\circ}$ about the origin, for any point $(x,y)$ on Figure A, its image $( - x,-y)$ will match the corresponding point on Figure B. The orientation of Figure A is upside - down and reversed in the x and y directions compared to Figure B, which is consistent with a $180^{\circ}$ counter - clockwise rotation about the origin.

Answer:

A counterclockwise rotation of 180 about the origin