What is the purpose of a dilation transformation?

A dilation transformation serves the specific purpose of resizing a shape by a scale factor. This transformation alters the size of the original figure but maintains its proportions and shape. During a dilation, each point of the shape moves away from or towards a fixed center point based on the scale factor; if the scale factor is greater than one, the figure expands, while a scale factor less than one leads to a reduction in size.

Maintaining the shape's proportions is crucial as it allows the figure to retain its similarity to the original, meaning the angles remain unchanged and the sides are scaled uniformly. This is vital in various fields like geometry, architecture, and design, where precise relationships between shapes are important. Dilation is distinct from other transformations like rotation, reflection, and translation, which do not involve resizing but rather altering location or orientation.