Question

the image (green) is the result of a transformation on the pre - image (blue). which transformation would accomplish this? figure u figure t a rotation 90° counterclockwise about the origin a reflection over the y - axis a rotation 90° clockwise about the origin a reflection over the x - axis

Explanation:

Step1: Observe coordinate changes

For a point $(x,y)$ in the pre - image (blue), in the image (green) the x - coordinate remains the same and the y - coordinate changes sign. For example, if a point in the blue figure is $(x,y)$, the corresponding point in the green figure is $(x, - y)$.

Step2: Recall transformation rules

The rule for a reflection over the x - axis is $(x,y)\to(x, - y)$. A 90° counter - clockwise rotation about the origin has the rule $(x,y)\to(-y,x)$, a 90° clockwise rotation about the origin has the rule $(x,y)\to(y, - x)$, and a reflection over the y - axis has the rule $(x,y)\to(-x,y)$. So, the transformation is a reflection over the x - axis.

Answer:

A reflection over the x - axis