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Dilation

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

If$\left|k\right|>1$, the dilation is an enlargement.

If$\left|k\right|<1$, the dilation is a reduction.

Theabsolute valueof the scale factor determines the size of the new image as compared to the size of the original image. When$k$是正新吗mage 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 producesimilar figures.