Which transformation involves dilation and contraction?

The correct answer is similarity transformations because they specifically encompass both dilation and contraction as part of their properties.

In the context of geometry, similarity transformations change the size of a figure but maintain its shape. This can be achieved through dilations, where a figure is enlarged (dilation) or reduced (contraction), producing a new figure that is proportionally similar to the original figure. For instance, if you have a triangle and you apply a dilation of scale factor greater than one, the triangle becomes larger but retains its angles and overall shape. Conversely, if you apply a scale factor between zero and one, the triangle shrinks but still remains similar to the original.

Other transformations, such as translation, reflection, and rotation, do not involve changes in size. They may move or flip the shape but do not alter its dimensions, meaning they lack the aspect of dilation and contraction that is central to similarity transformations. Thus, when identifying transformations that can dilate or contract a figure, similarity transformations are the key concept to focus on.