Call the rectangle R, the marked point P and the rectangle's center C. Draw a line segment PC to connect these points. Find the midpoint M between P and C. Now draw a rectangle Q that is entirely inside R, which has a pair of sides which are parallel to PC, has M as its center, and also contains P and C. This might need to be a very skinny rectangle if P is close to a corner (I assume P is an interior point). Q will have the same orientation as R only if P is directly above, below, left, or right of C.Now cut Q out of R. We now have two pieces: a smaller rectangle, and large rectangle with a hole. Pick up Q, rotate 180 degrees and place back in the hole. Now P and C have traded places. P is now in the center of the rectangular board.