What property does a direct isometry NOT have?

A direct isometry is a transformation that preserves essential geometric properties, meaning it maintains distances between points and keeps the shape and size of figures intact. Specifically, a direct isometry includes transformations such as translations, rotations, and reflections that do not alter the length of segments or the angles between lines.

The reason the assertion that a direct isometry "changes distance" is inaccurate is that one of the defining characteristics of isometries is that they preserve distances. For instance, if you take two points and apply a direct isometry, the distance between those two points will remain the same before and after the transformation.

In addition to preserving distance, direct isometries also maintain orientation, meaning the arrangement of points is consistent before and after the transformation. They also uphold the shape of figures, ensuring that all angles and relative lengths maintain their proportions. Therefore, the properties that characterize direct isometries revolve around the idea of preserving geometric relations rather than altering them.