Question

which of the following describes the transformation from the preimage to the image? a translation left 10 units a translation right 4 units a reflection over the y - axis a reflection over the x - axis

Explanation:

To determine the transformation, we analyze the coordinates (or positions) of points \( P \), \( Q \) (preimage) and \( P' \), \( Q' \) (image). A reflection over the \( x \)-axis changes the sign of the \( y \)-coordinate. Observing the graph, the preimage ( \( P, Q \)) and image ( \( P', Q' \)) appear to be mirrored over the \( x \)-axis (since the \( y \)-coordinates of corresponding points are negatives, while \( x \)-coordinates remain similar). Translations (left/right) would shift horizontally, but here the vertical flip (reflection over \( x \)-axis) matches. Reflections over \( y \)-axis flip horizontally, which is not the case. Translations (left 10 or right 4) don't fit as the vertical position changes sign, not horizontal shift.

Answer:

A. A reflection over the x - axis