Question

Point A is rotated 90 degrees counterclockwise around point C to form the image A'. Select three true statements based on the given information.

Answer 1

AC = A'C

A' lies on a circle centered at point C with radius AC

m∠ACA' = 90°

Explanation:

When we rotate a point A, around point C, the distance between the points is invariant.

This means that if A' es the image of the rotated point, then A' must lie in a circle centered in C with radius AC.

As we already defined, the distance between the rotated point and the center of rotation is invariant, then the distance between A and C must be the same as the distance between A' and C.

Answer 2

When we rotate a point A, around point C, the distance between the points is invariant.

This means that if A' es the image of the rotated point, then A' must lie in a circle centered in C with radius AC.

Then the correct statements are:

A' lies on a circle centered at point C with radius AC

This is by definition.

m∠ACA' = 90°

This is because A is rotated 90° around C to form the image A', then the measure must be 90°.

AC = A'C

As we already defined, the distance between the rotated point and the center of rotation is invariant, then the distance between A and C must be the same as the distance between A' and C.