Question

Regular hexagon ABCDEF rotates 240° counterclockwise about its center to produce hexagon A'B'C'D'E'F'. Which points will A' and B' coincide with in the preimage?

Answer 1

There are 360° around our hexagon.
Every 60° turn will turn one vertex to the next. (1/6 of the way around)
240° turns our point 4 times.
A' would go to C and B' would go to D. (note the counter-clockwise)
Draw yourself a diagram if it helps.
*note: You have to assume that the points are named clockwise around the hexagon