Pentagon A B C D E is reflected across the line of reflection m to pentagon A prime B prime C prime D prime E prime. Pentagon A prime B prime C prime D prime E prime is rotated about point C prime 180 degrees clockwise.

Question

Which rule describes the composition of transformations that maps figure ABCDE to figure A"B"C'D"E"?

90 degree rotation about point C prime composition reflected across line m
Reflected across line m composition 90 degree rotation about point C prime
180 degree rotation about point C prime composition reflected across line m
Reflected across line m composition 180 degree rotation about point C prime

Answer 1

To determine the correct description of the composition of transformations mapping pentagon ABCDE to A"B"C'D"E, we analyze the transformations step by step.

1. Reflection across line m: This transformation first reflects ABCDE to create A'B'C'D'E'.

2. 180 degree rotation about point C': After the reflection, the new pentagon A'B'C'D'E' is then rotated 180 degrees clockwise about point C'.

Now, we need to express this sequence using the correct notation. The order of transformations is important, and we typically express it in the order that the transformations occur from the original shape to the final shape.

The original shape ABCDE is first reflected across line m, producing the intermediate shape A'B'C'D'E'. Then, that intermediate shape is rotated about point C' by 180 degrees.

Therefore, we can summarize this as:

1. Reflected across line m (first step)
2. Composition with 180 degree rotation about point C' (second step)

So, the rule that describes the transformation from figure ABCDE to figure A"B"C'D"E is: Reflected across line m composition 180 degree rotation about point C prime.

Thus, the correct answer is: Reflected across line m composition 180 degree rotation about point C prime.