What is the value called that you must multiply lengths of a pre-image by to create the image in a dilation?

The value that you multiply the lengths of a pre-image by to create the image in a dilation is known as the scale factor. In geometry, dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The scale factor determines how much the image is enlarged or reduced compared to the original figure.

When the scale factor is greater than one, the image becomes larger than the original, and when it is less than one, the image becomes smaller. This concept helps in understanding relationships between similar figures, where corresponding lengths are proportional based on the scale factor. By using the scale factor, one can accurately determine new dimensions for the image while maintaining the same shape as the pre-image.