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 90° counterclockwise about the origin a rotation 180° clockwise about the origin a translation 2 units to the left and 2 units down this is a required question

Explanation:

Step1: Recall rotation rules

For a 180 - degree rotation about the origin (clockwise or counter - clockwise), the rule is $(x,y)\to(-x,-y)$.

Step2: Analyze the figures

By observing the pre - image (Figure A) and the image (Figure B), we can see that the orientation of the figure has changed in a way that is consistent with a 180 - degree rotation. For example, if we take a point on Figure A and its corresponding point on Figure B, the coordinates follow the $(x,y)\to(-x,-y)$ rule. A 90 - degree clockwise rotation has the rule $(x,y)\to(y, - x)$ and a 90 - degree counter - clockwise rotation has the rule $(x,y)\to(-y,x)$, which do not match the transformation here. Also, a translation 2 units to the left and 2 units down has the rule $(x,y)\to(x - 2,y - 2)$ which is not applicable as the orientation has changed. So, it is a 180 - degree clockwise rotation about the origin.

Answer:

A rotation 180° clockwise about the origin