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 directions

Translation down and to the right would move all points down - ward and right - ward. But the orientation of the shape has changed, so it's not a simple translation.

Step2: Analyze rotation about a point

By observing the orientation change of pre - image ABCD to image A''B''C''D'', we can see that it is a rotation. If we consider point B' as the center of rotation, a 180° rotation about point B' can map the pre - image to the image. A 270° rotation would change the orientation in a different way. And translations do not change the orientation of the shape.

Answer:

a 180° rotation about point B'