What is the primary difference between a rigid transformation and a non-rigid transformation?

The primary difference between rigid transformations and non-rigid transformations lies in how they affect the size and shape of figures. Rigid transformations—such as translations, rotations, and reflections—preserve both the size and shape of a geometric figure. This means that while the figure may change its position or orientation in space, its dimensions remain unchanged.

In contrast, non-rigid transformations, such as dilations or some forms of stretching, alter the size of the figure, which may also affect its shape. Because non-rigid transformations can change the scale of an object, they do not preserve the original measurements, resulting in figures that may appear distorted or different from their original form.

Thus, the correct understanding hinges on the fact that non-rigid transformations can indeed change the size of a figure, while rigid transformations maintain the original size and shape. This distinction is crucial in geometry, as it influences how we analyze and manipulate figures in various contexts.