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 counterclockwise rotation of 180° about the origin a reflection over the line y = x

Explanation:

Step1: Recall transformation rules

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

Step2: Analyze Figure A and Figure B

Let's take a point on Figure A, say the top - right vertex of Figure A which is approximately at $(-1,8)$.
If we apply a reflection over $y=-x$, $(-1,8)\to(-8,1)$.
If we apply a counter - clockwise rotation of $90^{\circ}$ about the origin, $(-1,8)\to(-8, - 1)$.
If we apply a counter - clockwise rotation of $180^{\circ}$ about the origin, $(-1,8)\to(1,-8)$.
If we apply a reflection over $y = x$, $(-1,8)\to(8,-1)$.
By observing the orientation and position of Figure A and Figure B, when we perform a counter - clockwise rotation of $180^{\circ}$ about the origin on each point of Figure A, we get the corresponding points of Figure B.

Answer:

A counterclockwise rotation of $180^{\circ}$ about the origin