Question

the image (green) is the result of a transformation on the pre - image (blue). which transformation would accomplish this? figure b figure a a rotation 90° clockwise about the origin a rotation 180° counterclockwise about the origin a translation 4 units to the left and 4 units up a reflection over the y - axis

Explanation:

Step1: Recall rotation rules

For a 90° clock - wise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$.

Step2: Analyze pre - image and image

If we take a point on Figure A (pre - image) and apply the 90° clockwise rotation rule about the origin, we can see that it maps to the corresponding point on Figure B. For example, if we consider a vertex of Figure A at say $(2,-2)$, after 90° clockwise rotation about the origin, using the rule $(y,-x)$ we get $(-2, - 2)$ which is consistent with the transformation from Figure A to Figure B.

Step3: Check other options

A 180° counter - clockwise rotation about the origin would change the orientation and position in a different way. A translation 4 units to the left and 4 units up would just shift the figure without rotating it. A reflection over the y - axis would flip the figure horizontally, not rotate it as shown.

Answer:

A. A rotation 90° clockwise about the origin