Also known as:

central dilation,

uniform scaling.

A central dilatation is sort of like mapping a flat shape onto a plane parallel to it via a lens. There's no distortion in shape (circles map to circles, not ellipses, etc.), and there's no rotation.
A mapping

*δ* on a

euclidian plane is a

__central dilatation__ iff *δ* is a

dilatation with a

fixed point, known as the

__dilatation center__ *C*.
Since

*δ* is a dilatation, it maps any line to a line parallel to it, and a vector changes by a nonzero scalar constant

*r* called the

__dilatation ratio__.
A central dilatation can be expressed as:

*δ*_{C,r}(*X*) = *r*(*X* - *C*) + *C* = *rX* + (1-*r*)*C*

Hence

*δ*_{C,r}(

*X*) is a

linear combination of

*X* and

*C*.
When the dilatation center happens to be on the

origin (

*C* = 0), the simpler expression is:

*δ*_{r}(*X*) = *rX*

Source:
"Vectors and Transformations in Plane Geometry" by Philippe Tondeur, Publish or Perish, Inc. 1993