Question

a composition of transformations maps pre - image efgh to final image efgh.
the first transformation for this composition is _, and the second transformation is a reflection across line e.
○ a 180° rotation about point g
○ a 180° rotation about point h
○ a translation down and to the left
○ a translation up and to the right

Explanation:

• A rotation about a point changes the orientation of the figure. A translation just slides the figure without rotation.
• If we consider the pre - image \(EFGH\) and the intermediate step before reflection across line \(c\), we can observe that the figure \(E'F'G'H'\) (the intermediate step) is obtained by rotating the pre - image \(EFGH\) about point \(H\).
• Rotation about point \(O\) would not map the figure in the way shown in the diagram. A translation (either up/down and left/right) would not change the orientation of the figure in the way that is consistent with the composition of transformations (since after translation, a reflection across line \(c\) would not give the final image as expected based on the orientation change from \(EFGH\) to \(E''F''G''H''\) if the first step was a translation).

Answer:

a \(180^{\circ}\) rotation about point \(H\)