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Dilation

A dilation (similarity transformation) is a transformation that changes the size of a figure.  It requires a center point and a scale factor, k.  The value of k determines whether the dilation is an enlargement or a reduction.

                        If |k| > 1, the dilation is an enlargement.

                        If |k| < 1, 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 k is positive the new image and the original image are on the same side of the center.  When k is negative they are on opposite sides of the center.  The center of a dilation is always its own image. 

Dilations preserve angle measure, betweeness of points and collinearity.  It does not preserve distance.  Simply, dilations always produce similar figures.