What is the definition of a direct isometry?

A direct isometry is a transformation that preserves both distances and the orientation of figures in the plane. This means that when a shape undergoes a direct isometry, the resulting figure is congruent to the original, and it retains the same arrangement of points. For example, rigid motions like translations and rotations are considered direct isometries because they keep the shape and size intact while maintaining the original orientation. In contrast, other transformations like reflections change the orientation of the figure, moving points to new locations that invert the structure. Therefore, the defining characteristic of a direct isometry is its ability to preserve orientation, alongside maintaining distances between points.