Question

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

Explanation:

Step1: Analyze Reflection over \(y = -x\)

A reflection over \(y=-x\) swaps and negates coordinates \((x,y)\to(-y,-x)\). Checking key points of Figure A, this doesn't match Figure B's position.

Step2: Analyze \(90^\circ\) Counterclockwise Rotation

A \(90^\circ\) counterclockwise rotation about the origin transforms \((x,y)\to(-y,x)\). This also doesn't align Figure A to B.

Step3: Analyze \(180^\circ\) Counterclockwise Rotation

A \(180^\circ\) counterclockwise rotation about the origin transforms \((x,y)\to(-x,-y)\). By checking the orientation and position of Figure A's vertices, rotating \(180^\circ\) counterclockwise about the origin maps Figure A to Figure B.

Step4: Analyze Reflection over \(y = x\)

A reflection over \(y = x\) swaps coordinates \((x,y)\to(y,x)\), which doesn't match the transformation from A to B.

Answer:

A counterclockwise rotation of \(180^\circ\) about the origin