Question

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

Explanation:

Step1: Analyze rotation by 180°

A 180° counterclockwise rotation about the origin transforms a point \((x,y)\) to \((-x,-y)\). Let's check a vertex of Figure A. For example, take a vertex of A (say, \((-6,-1)\)). After 180° rotation, it becomes \((6,1)\), which matches a vertex of Figure B.

Step2: Eliminate other options

• 90° counterclockwise rotation transforms \((x,y)\) to \((-y,x)\), which doesn't match B's vertices.
• Reflection over \(y = -x\) transforms \((x,y)\) to \((-y,-x)\), not matching.
• Reflection over \(y = x\) transforms \((x,y)\) to \((y,x)\), also not matching.

Answer:

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