Question

what is the final transformation in the composition of transformations that maps pre - image abcd to image a\bc\d\?
a translation up and to the right
a translation down and to the right
a 270° rotation about point b
a 180° rotation about point b

Explanation:

Step1: Observe the orientation change

By looking at the pre - image ABCD and the final image A''B'C''D'', we can see that the orientation of the shape has changed in a way that is characteristic of a rotation. The position of the vertices relative to each other has rotated around a point.

Step2: Analyze the rotation angle

If we consider point B' as a possible center of rotation, and compare the position of the pre - image relative to the final image, we can observe that the shape has been rotated 180°. A 270° rotation would result in a different orientation. Also, the shape has not just been translated (as translations do not change the orientation of the shape).

Answer:

a 180° rotation about point B'