A dilation (similarity transformation) is a transformation that changes the size of a figure. It requires a center point and a scale variable , k . The value the 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.

Tthat 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, betweenness of points and collinearity. It does not preserve distance. Simply, dilations always produce similar numbers .

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