Question

what is the final transformation in the composition of transformations that maps pre - image abcd to image a\b\c\d\? 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 options

Translation down and to the right would move all points down in the y - direction and right in the x - direction. Translation up and to the right would move all points up in the y - direction and right in the x - direction. But the transformation from A'B'C'D' to A''B''C''D'' is not a simple translation.

Step2: Analyze rotation options

A 270 - degree rotation about a point would change the orientation of the figure in a specific way. A 180 - degree rotation about a point (in this case B') would flip the figure across the center of rotation. By observing the orientation of pre - image A'B'C'D' and image A''B''C''D'', we can see that it is a 180 - degree rotation about point B'.

Answer:

a 180° rotation about point B'