Question

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

Explanation:

To determine the transformation, we analyze the positions of point \( A \) and its image \( A' \). A reflection over the \( y \)-axis changes the \( x \)-coordinate's sign (e.g., \((x,y) \to (-x,y)\)). A reflection over the \( x \)-axis changes the \( y \)-coordinate's sign (\((x,y) \to (x,-y)\)), which is not the case here. A translation left 10 units would move the point horizontally but the symmetry here suggests a reflection. A translation down 10 units moves vertically, which is not observed. The points \( A \) and \( A' \) are symmetric with respect to the \( y \)-axis, so the transformation is a reflection over the \( y \)-axis.

Answer:

A reflection over the \( y \)-axis