A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale factor , . The value of determines whether the dilation is an enlargement or a reduction.
If , the dilation is an enlargement.
If , the dilation is a reduction.
The absolute value of the scale factor determines the size of the new image as compared to the size of the original image. When is positive the new image and the original image are on the same side of the center. When is negative they are on opposite sides of the center. The center of a dilation is always its own image.
Dilations preserve angle measure, betweenness of points and collinearity. It does not preserve distance. Simply, dilations always produce similar figures .