Which transformation involves moving a figure around a fixed point?

The transformation that involves moving a figure around a fixed point is rotation. In a rotation, every point of the figure moves in a circular path around a central point, known as the center of rotation. The distance from each point on the figure to the center of rotation remains constant, while the angle of rotation determines how far around the center the points will move.

In contrast, translation shifts a figure from one location to another without changing its shape, size, or orientation, while reflection flips a figure over a line, producing a mirror image. Dilation changes the size of a figure while maintaining its shape, where the distances to a fixed point (the center of dilation) are scaled by a specific factor. Thus, rotation specifically involves the circular movement of points about a fixed center, making it the answer to the question.