In mathematics, a homothety is a transformation of an affine space determined by a point S called its center and a nonzero number k {\displaystyle k} called its ratio, which sends point X {\displaystyle X} to a point X ′ {\displaystyle X'} by the rule S X ′ → = k S X → {\displaystyle {\overrightarrow {SX'}}=k{\overrightarrow {SX}}} for a fixed number k ≠ 0 {\displaystyle k\neq 0}. Wikipedia