Question

which series of transformations will map rectangle abcd to rectangle abcd?

Explanation:

Step1: Analyze the vertical transformation

First, observe the vertical positions of the rectangles. Rectangle \(ABCD\) is above rectangle \(A'B'C'D'\). The distance between the corresponding points (e.g., \(D\) and \(D'\)) vertically is \(4\) units. A translation down by \(4\) units is needed.

Step2: Analyze the horizontal transformation

Next, consider the horizontal symmetry. After the vertical translation, we can see that the rectangles are mirror - images about the \(y\) - axis. A reflection across the \(y\) - axis will map the translated rectangle to \(A'B'C'D'\).

Answer:

Translate rectangle \(ABCD\) down \(4\) units and then reflect it across the \(y\) - axis.