Let O be a fixed point of the plane and k a given nonzero real number. By the dilatation (or expansion, or homothety, or stretch)  we mean the transformation of S onto itself which carries each point P of the plane into the point Q of the plane such that . The point O is called the center of the dilatation, and k is called the ratio of the dilatation.

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

The command with(geometry,dilatation) allows the use of the abbreviated form of this command.