Question

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

Explanation:

1. Analyze the first transformation (reflection or translation first):

• If we first reflect EFGH across line \( k \), the image (like \( E'F'G'H' \)) is formed. Then, translating this image down gives \( E''F''G''H'' \).
• For the other options: A translation down first would not align with the reflection's axis. A \( 180^\circ \) rotation about \( G \) would change the orientation in a way not matching the figure, and the order of translation and \( 180^\circ \) rotation also doesn't fit.

1. Confirm the correct sequence: The reflection across line \( k \) (vertical line) first flips the figure, then translating down matches the position of \( E''F''G''H'' \).

Answer:

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