Question

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

Explanation:

To determine the transformation, we analyze the positions of point \( A \) and its image \( A' \). A reflection over the \( y \)-axis changes the sign of the \( x \)-coordinate (e.g., \( (x,y) \to (-x,y) \)). A reflection over the \( x \)-axis changes the sign of the \( y \)-coordinate (\( (x,y) \to (x,-y) \)). A translation down or left would move the point vertically or horizontally without mirroring. By observing the grid, the transformation from \( A \) to \( A' \) is a reflection over the \( y \)-axis because the \( y \)-coordinate remains the same and the \( x \)-coordinate is negated (mirroring across the \( y \)-axis).

Answer:

A. A reflection over the y - axis