Question

compositions
which composition of transformations maps figure efgh to figure efgh?
a translation to the right followed by a 180° rotation about point g
a reflection across line k followed by a translation down
a 180° rotation about point g followed by a translation to the right
a translation down followed by a reflection across line k

Explanation:

Step1: Observe the first - stage transformation

We can see that figure EFGH first undergoes a reflection across line k to get to an intermediate figure (similar to E'F'G'H' but not exactly the same in position yet).

Step2: Observe the second - stage transformation

After the reflection across line k, the intermediate figure is then translated down to get to figure E''F''G''H''.

Answer:

a reflection across line k followed by a translation down