In what type of transformation do distances between points change?

In a dilation transformation, distances between points change because it involves resizing a shape either larger or smaller while maintaining its shape and proportions. When you apply a dilation, you use a scale factor that determines how much the figure expands or contracts. This means that the distances from the center of dilation to each of the points in the shape are multiplied by the scale factor, thus altering the relative distances between those points.

In contrast, reflections, translations, and rotations are isometric transformations, meaning they preserve distances and angles. A reflection flips a shape over a line, a translation slides it from one position to another without changing its size or shape, and a rotation turns a shape around a specific point at a constant distance from that point. In all these cases, the original distances between points in the shape remain unchanged, unlike in a dilation where the distances are affected by the scaling process.