Question

answer
a reflection over the x - axis
a reflection over the y - axis
a clockwise rotation of 90° about the origin
a clockwise rotation of 270° about the origin

Explanation:

1. For a reflection over the x - axis, the rule is $(x,y)\to(x, - y)$. Points of figure A would not transform to figure B this way.
2. For a reflection over the y - axis, the rule is $(x,y)\to(-x,y)$. Points of figure A would not transform to figure B this way.
3. For a clock - wise rotation of 90° about the origin, the rule is $(x,y)\to(y,-x)$. Points of figure A would not transform to figure B this way.
4. For a clock - wise rotation of 270° about the origin (which is equivalent to a counter - clockwise rotation of 90°), the rule is $(x,y)\to(-y,x)$. If we take the vertices of figure A and apply this transformation, we can see that figure A is transformed into figure B.

Answer:

D. A clockwise rotation of 270° about the origin