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 each option:

• Option 1: Reflecting EFGH over line \( k \) would map it to \( E'F'G'H' \) (the middle figure), then translating down would get to \( E''F''G''H'' \).
• Option 2: Translating down first would move EFGH below its original position, then reflecting over \( k \) wouldn't align with \( E''F''G''H'' \).
• Option 3: A \( 180^\circ \) rotation about \( G \) would change the orientation significantly, and translating right wouldn't match.
• Option 4: Translating right then rotating \( 180^\circ \) about \( G \) also doesn't align with the target figure.

1. The correct sequence is reflection across \( k \) (to get \( E'F'G'H' \)) then translation down (to get \( E''F''G''H'' \)).

Answer:

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