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: Observe the orientation change

Pre - image ABCD and image A''B'C''D'' have a 180 - degree change in orientation.

Step2: Check the center of rotation

By visual inspection, the center of rotation seems to be point B'.

Step3: Eliminate other options

Translation up/down and right/left would not change the orientation like this. A 270 - degree rotation would result in a different orientation than what is shown. So, it is a 180° rotation about point B'.

Answer:

a 180° rotation about point B'