Question

compositions
what is the final transformation in the composition of transformations that maps pre - image ghijk to image ghjk?
a reflection across line m
a 90° rotation about point g
a translation to the right
a 180° rotation about point g

Explanation:

Step1: Analyze the transformation from \( G'H'J'K' \) to \( G''H''J''K'' \)

Looking at the position of \( G'H'J'K' \) and \( G''H''J''K'' \), we check the transformation. The line \( m \) is vertical. Reflecting \( G'H'J'K' \) across line \( m \) (vertical line) would map it to \( G''H''J''K'' \). A rotation about \( G \) or translation doesn't match the orientation and position change as well as reflection across \( m \).

Step2: Eliminate other options

• A \( 90^\circ \) or \( 180^\circ \) rotation about \( G \) would change the orientation differently than seen.
• A translation to the right doesn't align with the mirror - like change across line \( m \).

Answer:

a reflection across line \( m \)