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 c. 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 translation changes the position of a figure without rotation or reflection.
• A rotation about a point changes the orientation of the figure.
• Looking at the pre - image \(EFGH\) and the intermediate image \(E'F'G'H'\), we can observe that the orientation of the figure \(EFGH\) and \(E'F'G'H'\) is the same. This indicates that a translation has occurred.
• If we consider the positions of the vertices of \(EFGH\) and \(E'F'G'H'\), we can see that the figure has moved down and to the left.

Answer:

a translation down and to the left