Which transformation maintains the distances between points in the transformed space?

The transformation that maintains distances between points in the transformed space is reflected in both reflections and rotations. These transformations are considered isometries, meaning that they preserve distances and angles, effectively keeping the geometric configuration of the figure unchanged.

When performing a reflection, points are flipped over a specified line (or hyperplane in higher dimensions), and the distance between any two points remains the same before and after the transformation. Similarly, a rotation involves turning the figure around a fixed point (the center of rotation), and it also preserves the distances between all points in the figure.

In contrast, projections typically do not maintain distances, as they often involve collapsing points onto a lower-dimensional subspace, which can change the distances between points. Therefore, both reflections and rotations qualify as transformations that preserve spatial relationships, making them the correct answer when combined.