Suppose one figure is mapped to a similar figure on the coordinate plane. The lengths of the sides the similar figure are twice the lengths of the corresponding sides of the original figure. In a sequence of transformations from the preimage to the image, which type of transformation must occur?

Answer 1

When one figure is mapped to a similar figure where the lengths of the sides are twice the lengths of the corresponding sides of the original figure, the transformation that must occur is a dilation.

A dilation is a transformation that produces an image that is the same shape as the original figure but is a different size. In this case, since the sides of the similar figure are twice the length of the original figure, the dilation factor is 2. This means that every point of the original figure is moved away from or towards a fixed center point (called the center of dilation) by a distance that is a multiple of the original distance, specifically two times that distance in this instance.

Therefore, the key transformation that must occur is a dilation with a scale factor of 2.