Octagon ABCDEFGH rotates 135° clockwise about its center to yield octagon A'B'C'D'E'F'G'H'. Which points will A' and B' coincide with from the preimage?

Question

aum · Answer

An octagon has 8 equal sides.
How much angle does each side make at the center?
8 sides together make 360 degrees at the center.
Therefore, each side makes 360/8 = 45 degrees at the center.
So if I rotate the octagon by 45 degrees around the center, A' will coincide with B from the preimage.  Rotate another 45 degrees for a total of 90 degrees rotation.  Then rotate another 45 degrees for a total of 135 degrees rotation.  Which points will A' and B' coincide with from the preimage?