Question

answer
a clockwise rotation of ( 270 ^ { circ } ) about the origin
a reflection over the line ( y = - x )
a reflection over the line ( y = x )
a clockwise rotation of ( 180 ^ { circ } ) about the origin

Explanation:

Step1: Recall reflection over \(y = -x\) rule

When reflecting a point \((x,y)\) over the line \(y=-x\), the transformation rule is \((x,y)\to(-y, -x)\).

Step2: Recall rotation rules

• For a \(270^{\circ}\) clock - wise rotation about the origin, the rule is \((x,y)\to(y,-x)\).
• For a \(180^{\circ}\) rotation about the origin, the rule is \((x,y)\to(-x,-y)\).
• For a reflection over \(y = x\), the rule is \((x,y)\to(y,x)\).

Step3: Analyze the figure

By comparing the position of the two polygons (A and B), if we take a general point \((x,y)\) on polygon A and check its image on polygon B. Using the transformation rules:
Let's assume a point \((a,b)\) on A. If after transformation it is \((-b,-a)\) (which is the rule for reflection over \(y=-x\)), and by visual inspection of the graph (checking the relative positions of vertices with respect to the line \(y =-x\)), we can confirm.

Answer:

A reflection over the line \(y=-x\)