An irregular parallelogram rotates 360 degrees about the midpint of its diagonal. how many times does the image of the parallelogram coincide with its preimage during the rotation

The "pre-image" is the original image before rotation. As you are rotating the irregular parallelogram about its midpoint, a 360-degree rotation means that it would just return to its original position. But it will also coincide at half of its full rotation, or at a 180-degree rotation. So all in all, it would coincide with its pre-image twice, or two times.

The answer would be a