Question

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: Analyze reflection across line \( k \)

First, check the reflection across line \( k \) (the vertical line). Reflecting \( EFGH \) over line \( k \) would map \( E \) to \( E' \), \( F \) to \( F' \), \( G \) to \( G' \), \( H \) to \( H' \), which matches the intermediate figure \( E'F'G'H' \) before the next transformation.

Step2: Analyze translation down

After reflecting across line \( k \), translating the figure down (vertically) would move \( E'F'G'H' \) to \( E''F''G''H'' \), as the vertical position of \( E'' \) (compared to \( E' \)) is lower, consistent with a downward translation.
Other options: A \( 180^\circ \) rotation about \( G \) would not align the figures, and the order of translation and reflection in other options doesn't match the visual transformation (reflection first, then translation down fits the path from \( EFGH \) to \( E'F'G'H' \) to \( E''F''G''H'' \)).

Answer:

a reflection across line \( k \) followed by a translation down