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

Math diagram

Math diagram

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