Question

what is the final transformation in the composition of transformations that maps pre-image abcd to image abcd? a translation down and to the right a 270° rotation about point b a translation up and to the right a 180° rotation about point b

Explanation:

To solve this, we analyze the transformation from \(A'B'C'D'\) to \(A''B''C''D''\):

1. Identify the type of transformation: A translation involves shifting a figure without rotating or reflecting it. A rotation involves turning the figure around a point.
2. Analyze the movement from \(A'B'C'D'\) to \(A''B''C''D''\):

• The figure \(A''B''C''D''\) appears to be shifted relative to \(A'B'C'D'\) (no rotation is visible, as the orientation of the sides/vertices remains consistent with a translation).
• Comparing the position of \(B'\) (a key vertex) to \(B''\), and other vertices, the figure moves up (vertically) and to the right (horizontally).

The transformation from \(A'B'C'D'\) to \(A''B''C''D''\) is a translation (no rotation, as orientation is preserved) that shifts the figure upward and to the right.

Answer:

a translation up and to the right