Which transformation is known as the only one that does not preserve orientation?

The transformation that is recognized as the only one that does not preserve orientation is a line reflection. When a shape is reflected across a line, the new image becomes a mirror image of the original. This can change the orientation of the shape, such as how the vertices or points are ordered around the center of the shape. For example, if you have a triangle, after reflecting it, the arrangement of its vertices would appear in reverse order, which signifies that the orientation has indeed changed.

In contrast, translations and rotations retain orientation. A translation shifts a shape in a straight line without altering its position or reflecting it, so all points maintain their original order. Similarly, a rotation turns a shape around a point but continues to keep the vertices in the same arrangement, preserving orientation. Similarity transformations, which include both dilations and rigid motions (like translations and rotations), also maintain orientation, as they involve scaling or moving a shape without flipping it. Hence, the distinct outcome observed during a line reflection highlights that it uniquely impacts the shape's orientation when compared to the other transformations.