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 rules

For a 180 - degree clock - wise rotation about the origin, the rule is $(x,y)\to(-x,-y)$.

Step2: Check key points

Let's assume a vertex of Figure A is $(x_1,y_1)$. After a 180 - degree clockwise rotation about the origin, it becomes $(-x_1,-y_1)$. By observing the positions of key vertices of Figure A and Figure B on the coordinate plane, we can see that the transformation follows the 180 - degree clockwise rotation rule about the origin.

Step3: Eliminate other options

For a 90 - degree clockwise rotation about the origin, the rule is $(x,y)\to(y, - x)$ which does not match. For reflection over $y=-x$, the rule is $(x,y)\to(-y,-x)$ and for reflection over $y = x$, the rule is $(x,y)\to(y,x)$, neither of which match the transformation from Figure A to Figure B.

Answer:

A. A clockwise rotation of 180° about the origin