Question

the image (green) is the result of a transformation on the pre - image (blue). which transformation would accomplish this? figure p figure q a translation 4 units up a reflection over the y - axis a reflection over the x - axis a translation 4 units down

Explanation:

Step1: Analyze translation

Translation moves a figure up, down, left or right without flipping it. Here the figure is flipped, so translation options (A and D) are incorrect.

Step2: Analyze reflection over y - axis

A reflection over the y - axis would change the x - coordinates of the points. But the x - coordinates of corresponding points in Figure P and Figure Q are the same, so option B is incorrect.

Step3: Analyze reflection over x - axis

For a point \((x,y)\) reflected over the x - axis, the new point is \((x, - y)\). In the given figures, the x - coordinates of corresponding points are the same and the y - coordinates are opposite in sign, which is characteristic of a reflection over the x - axis. So option C is correct.

Answer:

C. A reflection over the x - axis