Question

a composition of transformations maps pre - image efgh to final image e\f\g\h\. 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:

Step1: Analyze the orientation change

By observing the pre - image EFGH and the intermediate image E'F'G'H' (before reflection across line c), we can see that the orientation of the figure has changed in a way that is consistent with a rotation. A translation would not change the orientation of the figure.

Step2: Identify the rotation center

If we consider the rotation center, we can see that if we rotate the pre - image EFGH 180° about point H, the figure will be in the position of E'F'G'H'. Rotating about point G would not result in the correct intermediate position.

Answer:

a 180° rotation about point H