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 translation up and to the right a 270° rotation about point b a 180° rotation about point b

Explanation:

First, identify the pre-image ABCD (top right), intermediate A'B'C'D' (middle left), and final A''B''C''D'' (bottom left). The last step maps A'B'C'D' to A''B''C''D''. Observing point B' (fixed center), a 180° rotation about B' transforms A'B'C'D' to A''B''C''D'' (since 180° rotation reverses orientation and maps each point across B').

Answer:

a 180° rotation about point B'