Question

An n-sided polygon rotates 360° about its center, P. The image coincides with its preimage n times during the rotation. What can you conclude about this polygon?

A The polygon is a rectangle.


B The polygon is centered at the origin of a coordinate plane.


C The polygon is regular.


D The polygon is a parallelogram.

Answer 1

C The polygon is regular.

Answer 2

Option: C is the correct answer.

C The polygon is regular.

Explanation:

Regular Polygon--

A polygon is said to be regular if each of it's side are of equal length and each of it's angle are of equal measure.

i.e. it is a equilateral and equiangular.

Hence, the polygon with n sides has rotational symmetry of:
`(360)/(n)`

i.e. If the n-sided polygon rotates 360° about its center, P. The image coincides with its preimage n times during the rotation.

Hence, the answer is:

option: C