Homothety

In mathematics, a homothety (or homothecy) is a transformation of space which dilates distances with respect to a fixed point called the origin. The number by which distances are multiplied is called the dilation factor or similitude ratio.

Let us choose an origin or center and a real number (possibly negative). The homothety maps any point to a point such that (vectors here). In other words, are aligned and the (algebraic) distance is times the distance . (Algebraic means here that sign matters; for instance if then , which means that is on the other side of .)

A homothety is an affine transformation and more precisely a similarity transformation. It multiplies all distances by , all surfaces by , etc.