Question

answer
a counterclockwise rotation of 180° about the origin
a counterclockwise rotation of 270° about the origin
a reflection over the line y = -x
a reflection over the line y = x

Explanation:

Step1: Recall rotation and reflection rules

For a point \((x,y)\) rotated counter - clockwise \(180^{\circ}\) about the origin, the new point is \((-x,-y)\). For a counter - clockwise rotation of \(270^{\circ}\) about the origin, the transformation is \((x,y)\to(y, - x)\). For a reflection over the line \(y=-x\), the transformation is \((x,y)\to(-y,-x)\) and for a reflection over the line \(y = x\), the transformation is \((x,y)\to(y,x)\).

Step2: Analyze the orientation of the shapes

The orientation of the two shapes (the blue and the pink ones) is such that if we consider a general point \((x,y)\) on the blue shape, the corresponding point on the pink shape has coordinates \((y,-x)\) which is the rule for a counter - clockwise rotation of \(270^{\circ}\) about the origin.

Answer:

A counterclockwise rotation of \(270^{\circ}\) about the origin