Dilation (geometry)

a special geometric transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions according to a centric point

In geometry, dilation (also called homothety or homothetic transformation) is the process which changes the size of a figure without changing its shape, a type of transformation. Any figure and its image after dilation are similar to each other.

Two similar geometric figures related by a dilation, with the center of dilation at S.

Dilation is defined by a point V, the center of dilation, and a number k, the ratio. Given a point P in the plane, its image P' (P prime) is on the line VP. The distance from P' to V is k times the distance from P to V.


  • Pedoe, Dan (1988), Geometry: A Comprehensive Course, New York: Dover Publications, p. 56-57, ISBN 0-486-65812-0
  • Meserve, Bruce E. (1955), "Homothetic transformations", Fundamental Concepts of Geometry, Addison-Wesley, pp. 166–169

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