Question

the image (green) is the result of a transformation on the pre - image (blue). which transformation would accomplish this? figure f figure e a translation 4 units to the left and 4 units down a rotation 90° counterclockwise about the origin a rotation 180° clockwise about the origin a rotation 90° clockwise about the origin

Explanation:

Step1: Recall rotation rules

For a 90 - degree clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(y, - x)$.

Step2: Check key - points

Take a key - point of Figure E, say $(4,1)$. After a 90 - degree clockwise rotation about the origin, using the rule $(x,y)\to(y, - x)$, we get $(1,-4)$. Looking at Figure F, we can see that the transformation of key - points of Figure E to Figure F follows the 90 - degree clockwise rotation rule about the origin.

Step3: Eliminate other options

A translation 4 units to the left and 4 units down would move all points in a linear non - rotational way. A 90 - degree counter - clockwise rotation rule is $(x,y)\to(-y,x)$ and a 180 - degree clockwise rotation rule is $(x,y)\to(-x,-y)$, which do not match the transformation from Figure E to Figure F.

Answer:

D. A rotation 90° clockwise about the origin