Question

a dilation is a nonrigid transformation that can produce enlarged or reduced images from a given pre - image. how do you know that a dilation will produce similar figures? explain.

Explanation:

A dilation is a transformation that changes the size of a figure but not its shape. Similar figures have the same shape but not necessarily the same size. In a dilation, the corresponding angles of the pre - image and the image are equal (since the shape is preserved), and the ratios of the lengths of the corresponding sides are equal (determined by the scale factor of the dilation). By the definition of similar figures (equal corresponding angles and proportional corresponding sides), a dilation produces similar figures.

Answer:

A dilation produces similar figures because it preserves the shape of the pre - image.