Question

what is the final transformation in the composition of transformations that maps pre - image ghj k to image ghjk?
a translation to the right
a reflection across line m
a 90° rotation about point g
a 180° rotation about point g

Explanation:

Step1: Observe the orientation change

Pre - image GHJK and image G'H'J'K' have a change in orientation. Comparing the relative positions of the vertices of the two shapes, we can see that it is not a simple translation (no sliding without rotation or reflection).

Step2: Analyze the possible rotation

If we consider point G as a pivot point, we can see that the shape has been rotated. The pre - image and image have an orientation difference that is consistent with a 180° rotation about point G. A 90° rotation would result in a different orientation. Also, there is no indication of a reflection across line m as the shape's orientation is not a mirror - like flip across that line.

Answer:

a 180° rotation about point G