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:

Step1: Analyze translation characteristics

Translation moves a figure without rotation. Observing the pre - image and image, it's not a simple translation as the orientation has changed.

Step2: Analyze rotation around point B'

Count the angle of rotation of corresponding points around B'. We can see that the pre - image ABCD is rotated 180° around point B' to get to the final position. A 270° rotation would change the orientation in a different way.

Answer:

a 180° rotation about point B'