In math, a homothety  is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio

in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similitaries that fix a point and either preserve (if λ > 0) or reverse (if λ < 0) the direction of all vectors. Together with the translations, all homotheties of an affine space form a group, the group of homothety-translations. These are precisely the affine transformations with the property that the image of every line L is a line parallel to L.