Question

compositions
which composition of transformations maps figure efgh to figure efgh?
options:

• a 180° rotation about point g followed by a translation to the right
• a reflection across line k followed by a translation down
• a translation down followed by a reflection across line k
• a translation to the right followed by a 180° rotation about point g

Explanation:

1. First, observe the vertical movement: Figure \( EFGH \) needs to move down to align vertically with \( E''F''G''H'' \) (since \( E''F''G''H'' \) is below \( EFGH \) relative to line \( k \)).
2. Then, a reflection across line \( k \) (the horizontal line) would flip the translated figure to match the orientation of \( E''F''G''H'' \).
3. Other options: A \( 180^\circ \) rotation about \( G \) would change the shape's orientation incorrectly. A translation right or reflection first then translation down doesn't match the vertical - horizontal transformation sequence needed.

Answer:

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