Scale factor

A scale factor (k) is a value used in a dilation. Every dilation must have a center and a scale factor. The scale factor goes to how the image is related to the preimage during the dilation. In a dilation, every point of the image must fall along a line connecting the center of dilation to the corresponding point of the preimage. The scale factor controls how the image is formed from the preimage. Because of this, the scale factor is an important part of every dilation. Dilations always result in an image that is similar to the preimage. The image and preimage have the same shape. The scale factor is the value that relates the image to the preimage. If the scale factor changes, the size of the image changes as well. There is one time where the scale factor becomes special. When the scale factor equals 1, the image is congruent to the preimage. In this situation, the dilation does not change the size of the figure. The image is both similar and congruent to the original figure.