Question

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

Explanation:

Step1: Recall rotation and reflection rules

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

Step2: Analyze the transformation visually

Let's assume a vertex of Figure A is $(x_1,y_1)$. By observing the orientation and position change from Figure A to Figure B, we can test the transformation rules on the vertices. If we take a general point $(x,y)$ of Figure A and consider a reflection over the line $y = -x$. If we have a point $(x,y)$ in Figure A, after reflection over $y=-x$, the new point is $(-y,-x)$. Visually, the orientation and position of Figure B relative to Figure A match the result of reflection over $y = -x$.

Answer:

A reflection over the line $y=-x$