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geometry

 dilatation
 find the dilatation of a geometric object
 expansion
 find the expansion of a geometric object
 homothety
 find the homothety of a geometric object
 stretch
 find the stretch of a geometric object

 Calling Sequence dilatation(Q, P, k, O) expansion(Q, P, k, O) homothety(Q, P, k, O) stretch(Q, P, k, O)

Parameters

 Q - the name of the object to be created P - geometric object k - number which is the ratio of the dilatation O - point which is the center of the dilatation

Description

 • 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 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{point}\left(A,1,1\right):$$\mathrm{dilatation}\left(B,A,3,\mathrm{point}\left(\mathrm{OO},3,3\right)\right):$
 > $\mathrm{detail}\left(B\right)$
 $\begin{array}{ll}{\text{name of the object}}& {B}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[{-3}{,}{-3}\right]\end{array}$ (1)

define the circle with center at (0,0) and radius 1

 > $\mathrm{circle}\left(c,\left[\mathrm{point}\left(\mathrm{OO},0,0\right),1\right]\right):$
 > $\mathrm{homothety}\left(\mathrm{c1},c,3,\mathrm{OO}\right):$
 > $\mathrm{draw}\left(\left\{c\left(\mathrm{color}=\mathrm{red},\mathrm{style}=\mathrm{POINT},\mathrm{symbol}=\mathrm{DIAMOND}\right),\mathrm{c1}\left(\mathrm{color}=\mathrm{blue},\mathrm{style}=\mathrm{POINT},\mathrm{symbol}=\mathrm{CROSS},\mathrm{numpoints}=100\right)\right\},\mathrm{title}=\mathrm{dilatation of a circle}\right)$ define the parabola with vertex at (0,0) and focus at (0,1/2)

 > $\mathrm{parabola}\left(\mathrm{p1},\left['\mathrm{vertex}'=\mathrm{point}\left('\mathrm{ver}',0,0\right),'\mathrm{focus}'=\mathrm{point}\left('\mathrm{fo}',0,\frac{1}{2}\right)\right]\right):$
 > $\mathrm{expansion}\left(\mathrm{p2},\mathrm{p1},2,\mathrm{OO}\right):$
 > $\mathrm{expansion}\left(\mathrm{p3},\mathrm{p1},\frac{1}{2},\mathrm{OO}\right):$
 > $\mathrm{expansion}\left(\mathrm{p4},\mathrm{p1},\frac{1}{4},\mathrm{OO}\right):$
 > $\mathrm{draw}\left(\left[\mathrm{p1}\left(\mathrm{color}=\mathrm{green},\mathrm{style}=\mathrm{LINE},\mathrm{thickness}=2\right),\mathrm{p2},\mathrm{p3},\mathrm{p4}\right],\mathrm{style}=\mathrm{POINT},\mathrm{color}=\mathrm{brown},\mathrm{view}=\left[-\frac{1}{2}..\frac{1}{2},0...\frac{2}{5}\right],\mathrm{numpoints}=400,\mathrm{title}=\mathrm{dilatation of a hyperbola}\right)$ 