Question

answer
a rotation 90° counterclockwise about the origin
a rotation 90° clockwise about the origin
a reflection over the x - axis
a reflection over the y - axis
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Explanation:

Step1: Recall transformation rules

A 90 - degree counter - clockwise rotation about the origin has the rule $(x,y)\to(-y,x)$. A 90 - degree clockwise rotation about the origin has the rule $(x,y)\to(y, - x)$. A reflection over the $x$ - axis has the rule $(x,y)\to(x,-y)$. A reflection over the $y$ - axis has the rule $(x,y)\to(-x,y)$.

Step2: Analyze the transformation from Figure A to Figure B

If we take a point on Figure A, say $(x,y)$, and observe its corresponding point on Figure B, we can see that the transformation is $(x,y)\to(-x,y)$. This is the rule for a reflection over the $y$ - axis.

Answer:

A reflection over the $y$-axis