Question

a composition of transformations maps pre - image efgh to final image efgh. the first transformation for this composition is , and the second transformation is a reflection across line c.
a translation up and to the right
a 180° rotation about point h
a translation down and to the left
a 180° rotation about point g

Explanation:

Step1: Analyze transformation composition

The problem involves mapping pre-image EFGH to final image E''F''G''H'' via two transformations: first transformation (unknown) then reflection across line c.

Step2: Evaluate options for first transformation

Key is how the first transformation relates EFGH to intermediate E'F'G'H' before reflection. A 180° rotation about a fixed point (e.g., G) would flip the figure, and subsequent reflection across line c would produce the final image, matching typical geometric transformation compositions.

Answer:

a 180° rotation about point G