In a transformation, what does preserving distance mean?

Preserving distance in a transformation refers to maintaining the original lengths of all segments and the overall geometric integrity of the shape. This concept is critical in transformations such as translations, rotations, and reflections, which are classified as isometric transformations because they do not change the size of the shapes involved.

When we say that distance is preserved, it means that if you measure a segment in the original shape, the corresponding segment in the transformed shape will have the same length. This is why the correct answer highlights that the shape stays the same size. While rotations and reflections can alter the orientation of a shape, they do not change its size or distance between points. Conversely, compression would involve altering a shape's dimensions, violating the principle of distance preservation. Therefore, the definition aligns with the concept that transformations maintaining distance ensure that the overall dimensions remain unchanged.