Question

Triangle JKL is transformed by performing a 90degree clockwise rotation about the origin and then a reflection over the y-axis, creating triangle J’’K’’L’’. Which transformation will map J’’K’’L’’ back to JKL?
a reflection over the y-axis and then a 90degree clockwise rotation about the origin
a reflection over the x-axis and then a 90degree counterclockwise rotation about the origin
a reflection over the x-axis and then a 90degree clockwise rotation about the origin
a reflection over the x-axis and then a reflection over the y-axis

Answer 1

Compute the effect on a point (x,y).

90° clockwise: (x,y) → (y, −x).
Reflect over the y-axis: (y, −x) → (−y, −x).

So J → J'' is (x,y) → (−y, −x). To undo that, start with (−y, −x): reflect over the x-axis gives (−y, x), then rotate 90° clockwise gives (x,y).

Thus the correct choice is: a reflection over the x-axis and then a 90° clockwise rotation about the origin.