Question

Banish Claims that a reflection over the x-axis will carry a circle drawn on a coordinate plane to a circle with the same radius but with a different center. He draws four circles on a coordinate plane below.

Answer 1

If you do a reflection on the x-axis, you're taking the points from (x , y) to (x , -y).

The only case where the circle won't change its center it is when the center is located at the x-axis(when y = 0).

From the examples given in the question, only the circle C won't change its center.

The answer would be:

Circle A: Support

Circle B: Support

Circle C: Refute

Circle D: Support