Question

The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point ? of the preimage. Point D′ of the image coincides with point ? of the preimage.

Answer 1

The correct answer to this question is points C' and D'

If I turn it 60 degrees counterclockwise, the A will be where F is
If i turn it 120 degrees counterclockwise, the A will be where E is..
If you continue this pattern,

The point C will coincide where A is before.
The point D will coincide where B is before.

Answer 2

Point C′ of the image coincides with point E of the preimage.

Point D′ of the image coincides with point F of the preimage.

Explanation:

A translation counterclockwise 60° moves point A to F, F to E, E to D, et cetera. A translation counterclockwise 180° moves any vertex to the opposite vertex, so A moves to D, B to E, C to F and vice versa. Then, a translation counterclockwise 240° is a combination of the two aforementioned translations and moves A to C, F to B, E to A, D to F, C to E and B to D, creating the hexagon A′B′C′D′E′F′ (see figure attached).