Which transformation results in a figure turning about a pivot point without changing its shape?

The transformation that results in a figure turning about a pivot point without changing its shape is rotation. When a figure is rotated, every point in the figure moves in a circular path around a fixed point, known as the center of rotation, without altering the size or shape of the figure itself. This maintains the original dimensions and angles of the figure while changing its position and orientation in the plane.

In a rotation, the distance from the pivot point to any point on the figure remains constant, ensuring that only the direction of the figure changes. This is key to understanding why rotation specifically is about turning rather than changing the figure in other ways.

In contrast, other transformations such as dilation involve changing the size of the figure, reflection flips the figure over a line, and translation shifts the figure from one location to another without rotating it. These transformations alter the figure in a way that is not consistent with the requirements of the question.