Question

what is the final transformation in the composition of transformations that maps pre-image ghjk to image g\h\j\k\?

a translation to the right
a reflection across line m
a 90° rotation about point g
a 180° rotation about point g

Explanation:

Analyze the first transformation

Using the Composition of Transformations knowledge point
The pre-image is \(GHJK\). The intermediate image is \(G'H'J'K'\) (labeled as \(G, H', J', K'\) where \(G\) is shared).
Observing the orientation, \(GHJK\) is rotated counterclockwise about point \(G\) by \(90^\circ\) to become \(G'H'J'K'\).

Analyze the final transformation

The intermediate image \(G'H'J'K'\) is on the right side of the vertical line \(m\).
The final image \(G''H''J''K''\) is on the left side of the vertical line \(m\).
Every point of \(G''H''J''K''\) is a mirror image of \(G'H'J'K'\) across the vertical line \(m\).
Thus, the final transformation mapping \(G'H'J'K'\) to \(G''H''J''K''\) is a reflection across line \(m\).

Answer:

• a translation to the right
• a reflection across line m (Correct answer)
• a 90° rotation about point G
• a 180° rotation about point G