Question

which of the following describes the transformation from the preimage to the image? a translation down 8 units a translation down 4 units a reflection over the y - axis a reflection over the x - axis

Explanation:

To determine the transformation, we analyze the positions of points \( S, T \) and their images \( S', T' \). A reflection over the \( y \)-axis changes the \( x \)-coordinate's sign (e.g., \((x,y) \to (-x,y)\)). Observing the graph, the preimage and image points seem symmetric with respect to the \( y \)-axis. Translations (down 8 or 4 units) would shift points vertically, but here the symmetry is horizontal (over \( y \)-axis), not vertical shift. Reflection over \( x \)-axis would flip \( y \)-coordinates, which doesn't match. So the transformation is a reflection over the \( y \)-axis.

Answer:

B. A reflection over the y - axis