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) $H\left(\mathrm{O}\,k\right)$ we mean the transformation of the plane S onto itself which carries each point P of the plane into the point Q of the plane such that $\mathrm{SensedMagnitude}\left(\mathrm{OQ}\right)=k\mathrm{SensedMagnitude}\left(\mathrm{OP}\right)$. 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.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(A\,1\,1\right)\:$$\mathrm{dilatation}\left(B\,A\,3\,\mathrm{point}\left(\mathrm{OO}\,3\,3\right)\right)\:$

$\mathrm{detail}\left(B\right)$

$\begin{array}{ll}\text{name of the object}& B\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[\mathrm{-3}\,\mathrm{-3}\right]\end{array}$

$\mathrm{circle}\left(c\,\left[\mathrm{point}\left(\mathrm{OO}\,0\,0\right)\,1\right]\right)\:$

$\mathrm{homothety}\left(\mathrm{c1}\,c\,3\,\mathrm{OO}\right)\:$

$\mathrm{draw}\left(\left\{c\left(\mathrm{color}\=\mathrm{red}\,\mathrm{style}\=\mathrm{POINT}\,\mathrm{symbol}\=\mathrm{DIAMOND}\right)\,\mathrm{c1}\left(\mathrm{color}\=\mathrm{blue}\,\mathrm{style}\=\mathrm{POINT}\,\mathrm{symbol}\=\mathrm{CROSS}\,\mathrm{numpoints}\=100\right)\right\}\,\mathrm{title}\=\mathrm{`dilatation\; of\; a\; circle`}\right)$

$\mathrm{parabola}\left(\mathrm{p1}\,\left[\'\mathrm{vertex}\'\=\mathrm{point}\left(\'\mathrm{ver}\'\,0\,0\right)\,\'\mathrm{focus}\'\=\mathrm{point}\left(\'\mathrm{fo}\'\,0\,\frac{1}{2}\right)\right]\right)\:$

$\mathrm{expansion}\left(\mathrm{p2}\,\mathrm{p1}\,2\,\mathrm{OO}\right)\:$

$\mathrm{expansion}\left(\mathrm{p3}\,\mathrm{p1}\,\frac{1}{2}\,\mathrm{OO}\right)\:$

$\mathrm{expansion}\left(\mathrm{p4}\,\mathrm{p1}\,\frac{1}{4}\,\mathrm{OO}\right)\:$

$\mathrm{draw}\left(\left[\mathrm{p1}\left(\mathrm{color}\=\mathrm{green}\,\mathrm{style}\=\mathrm{LINE}\,\mathrm{thickness}\=2\right)\,\mathrm{p2}\,\mathrm{p3}\,\mathrm{p4}\right]\,\mathrm{style}\=\mathrm{POINT}\,\mathrm{color}\=\mathrm{brown}\,\mathrm{view}\=\left[-\frac{1}{2}..\frac{1}{2}\,0.0..\frac{2}{5}\right]\,\mathrm{numpoints}\=400\,\mathrm{title}\=\mathrm{`dilatation\; of\; a\; hyperbola`}\right)$