Question

Harold argues that a semi-circle has rotation symmetry, but Jay disagrees. Who is correct and why?

Answer 1

See below.

Explanation:

Jay is correct.

If you draw a semicircle with a diameter and use the center of the circle as the point of rotation, the figure will only look the same as the original when it is rotated 360 degrees. This gives the semicircle an order of rotation of 1. That means that once you start rotating a semicircle, it only looks like itself after a full 360-degree rotation. It does not have rotational symmetry.