Question

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

1. Recall transformation rules:

• For a 180 - degree clock - wise rotation about the origin, the rule for a point \((x,y)\) is \((x,y)\to(-x,-y)\).
• For a reflection over the line \(y = x\), the rule is \((x,y)\to(y,x)\).
• For a 270 - degree clock - wise rotation about the origin, the rule for a point \((x,y)\) is \((x,y)\to(y, - x)\).
• For a reflection over the line \(y=-x\), the rule is \((x,y)\to(-y,-x)\).

1. Analyze the given figures:

• By observing the orientation and position of figure A and figure B, we can check each transformation.
• A 270 - degree clock - wise rotation about the origin maps figure A to figure B. For example, if we take a vertex of figure A with coordinates \((x,y)\), after a 270 - degree clock - wise rotation about the origin, its new coordinates \((y,-x)\) match the corresponding vertex of figure B.

Answer:

A clockwise rotation of 270° about the origin