Question

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

Explanation:

Step1: Recall rotation rules

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

Step2: Analyze figure transformation

Comparing Figure B and Figure C, we can see that the orientation and position of the figure match the pattern of a 90° counter - clockwise rotation about the origin. For example, if we consider key points of Figure B and their corresponding points in Figure C, they follow the (-y,x) rule.

Step3: Eliminate other options

A translation 4 units to the right and 4 units down/up or 4 units to the left and 4 units up would just shift the figure without rotating it. A 90° clockwise rotation about the origin has a different transformation rule (x,y)→(y, - x) which does not match the given transformation.

Answer:

A rotation 90° counter - clockwise about the origin