What type of transformation maintains the size and shape of a figure?

The type of transformation that maintains both the size and shape of a figure is known as a rigid transformation. Rigid transformations include operations such as translations, rotations, and reflections, which do not alter the dimensions or proportions of the figure. Instead, these transformations reposition the figure in space while preserving its overall characteristics, meaning that the distance between points and the angles within the figure remain unchanged.

In contrast, other transformations like dilations, stretching, and skewing involve altering the figure's size, shape, or both. For example, a dilation changes the size of a figure by a scale factor, which can either enlarge or reduce it but does not preserve the shape. Stretching modifies the dimensions of the figure disproportionately, resulting in changes to its proportions. Skewing distorts the figure by slanting it in one direction, further affecting both its shape and size. Hence, the only type of transformation that keeps the figure unchanged in size and shape is the rigid transformation.