A dilation is a similarity transformation that maps each line to a parallel line whose length is a fixed multiple of the original line's length. The simplest dilation is therefore a translation, and any dilation that is not merely a translation is called a central dilation. Two triangles related by a central dilation are said to be perspective triangles because the lines joining corresponding vertices concur. A dilation corresponds to an expansion plus a translation.

See also

Affine Transformation, Expansion, Graph Dilation, Parallel, Perspective Triangles, Translation

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References

Coxeter, H. S. M. and Greitzer, S. L. "Dilation." §4.7 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 94-95, 1967.

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Dilation

Cite this as:

Weisstein, Eric W. "Dilation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Dilation.html

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