Question

determine a series of transformations that would map polygon abcde onto polygon abcde?

Explanation:

Step1: Observe orientation change

The polygon ABCDE is reflected across the y - axis to change its orientation to match that of A'B'C'D'E'. A reflection across the y - axis changes the sign of the x - coordinates of all the points while keeping the y - coordinates the same. For a point (x,y) in polygon ABCDE, after reflection across the y - axis, it becomes (-x,y).

Step2: Observe vertical movement

After reflection, the polygon needs to be translated down. Counting the vertical distance between a corresponding point (e.g., point A and A') after reflection and before the final position, we find that the polygon is translated 5 units down. A translation 5 units down changes the y - coordinate of each point by subtracting 5. So a point (x,y) after reflection becomes (x,y - 5).

Answer:

A reflection across the y - axis followed by a translation 5 units down.