Question

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

Explanation:

To determine the transformation, we analyze the coordinates of points \( P \) and \( P' \), \( Q \) and \( Q' \). A reflection over the \( x \)-axis changes the sign of the \( y \)-coordinate. Observing the graph, the preimage (e.g., \( P \)) and image (e.g., \( P' \)) have \( x \)-coordinates the same and \( y \)-coordinates with opposite signs, indicating a reflection over the \( x \)-axis. Translations would involve moving horizontally or vertically, and reflection over \( y \)-axis would change \( x \)-coordinate sign, which is not the case here.

Answer:

A. A reflection over the x - axis