Question

regular hexagon abcdef is inscribed in a circle with center h.
a. what is the image of segment ab after a 120 - degree clockwise rotation about point h?
b. what is the image of segment ab after a reflection over line fc? segment options: ab, bc, cd, de, ef, fa

Explanation:

Step1: Analyze rotation in regular hexagon

In a regular hexagon, the central angle between two consecutive vertices is $\frac{360^{\circ}}{6}=60^{\circ}$. A 120 - degree clockwise rotation about the center $H$ moves the segment by two vertices clock - wise. Starting from segment $AB$, after a 120 - degree clockwise rotation about $H$, the image is segment $CD$.

Step2: Analyze reflection in regular hexagon

The line $FC$ is a line of symmetry of the regular hexagon. Segment $AB$ and segment $ED$ are symmetric about the line $FC$. So the image of segment $AB$ after reflection over line $FC$ is segment $ED$.

Answer:

a. Segment CD
b. Segment DE