Question

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.
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

"180 degree rotation about point C' composition reflected across line m."

Reason: the pentagon is first reflected across line m (giving A'B'C'D'E') and then that image is rotated 180° about C' to produce A" B" C" D" E". In composition notation, apply the reflection first, then the 180° rotation.