Question

which transformation would take figure a to figure b? answer a counterclockwise rotation of 90° about the origin a reflection over the y - axis a counterclockwise rotation of 270° about the origin a reflection over the x - axis

Explanation:

Step1: Recall reflection rule

A reflection over the y - axis changes the sign of the x - coordinate of each point while keeping the y - coordinate the same. For a point $(x,y)$ it becomes $(-x,y)$.

Step2: Observe figure

In the given graph, Figure A and Figure B are mirror - images of each other with respect to the y - axis. Points on Figure A and their corresponding points on Figure B have x - coordinates with opposite signs and y - coordinates that are the same.

Step3: Check other transformations

A counter - clockwise rotation of 90° about the origin changes a point $(x,y)$ to $(-y,x)$. A counter - clockwise rotation of 270° about the origin changes a point $(x,y)$ to $(y, - x)$. A reflection over the x - axis changes a point $(x,y)$ to $(x, - y)$. These do not match the transformation from Figure A to Figure B.

Answer:

B. A reflection over the y - axis