What preservation occurs in a direct isometry?

In a direct isometry, both distance and direction are preserved. This means that when a shape undergoes a direct isometry, such as a translation or a rotation, the size and spacing between all points remain the same; that is, the distances between points are unchanged. Additionally, the orientation of the shape is maintained—what was to the left remains to the left after the transformation, for instance.

Direct isometries do not involve any flipping or reflecting of the shape; therefore, the direction remains the same as it was before the transformation. This guarantees that every feature of the shape retains its properties, leading to the conclusion that both distance and direction are preserved in a direct isometry.