Question

select the correct answer. a regular octagon rotates 360° about its center. how many times does the image of the octagon coincide with the preimage during the rotation? a. 1 b. 2 c. 4 d. 8

Explanation:

Step1: Recall rotational symmetry concept

A regular polygon has rotational symmetry. For a regular \(n -\)sided polygon, the angle of rotation for which the polygon coincides with its pre - image is given by \(\theta=\frac{360^{\circ}}{n}\).

Step2: Identify \(n\) for an octagon

An octagon has \(n = 8\) sides.

Step3: Calculate number of coincidences

The number of times a regular \(n -\)sided polygon coincides with its pre - image when rotated \(360^{\circ}\) about its center is equal to \(n\). Since \(n = 8\) for an octagon, it will coincide with its pre - image 8 times during a \(360^{\circ}\) rotation.

Answer:

D. 8