Homothety

The homothety of point \(M\) with center \(O\) and scale factor \(\textcolor{olive}{k}\) is the point \(M'\) such that \(\overrightarrow{OM'}=\textcolor{olive}{k}\overrightarrow{OM}\). In particular, the points \(O\), \(M\), and \(M'\) lie on the same line, and the distance from \(O\) to \(M'\) is \(|\textcolor{olive}{k}|\) times the distance from \(O\) to \(M\).
\(\dfrac{\textcolor{colorprop}{OM'}}{\textcolor{colordef}{OM}}=|\textcolor{olive}{k}|\)

Find the coordinates of the image of point \(M\) under a homothety with center \(O\) and scale factor \(k=2\).

The homothety of a figure with center \(O\) and scale factor \(k\) is the image obtained by applying the homothety with center \(O\) and scale factor \(k\) to all its points.

The figure \(\textcolor{colorprop}{A'}\) is the image of figure \(\textcolor{colordef}{A}\) under a homothety with center \(O\) and scale factor \(2\).