find the dilatation of a geometric object
find the expansion of a geometric object
find the homothety of a geometric object
find the stretch of a geometric object
dilatation(Q, P, k, O)
expansion(Q, P, k, O)
homothety(Q, P, k, O)
stretch(Q, P, k, O)
the name of the object to be created
number which is the ratio of the dilatation
point which is the center of the dilatation
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⁡O,k 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 SensedMagnitude⁡OQ=k⁢SensedMagnitude⁡OP. 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.
name of the objectBform of the objectpoint2dcoordinates of the point−3,−3
define the circle with center at (0,0) and radius 1
draw⁡c⁡color=red,style=POINT,symbol=DIAMOND,c1⁡color=blue,style=POINT,symbol=CROSS,numpoints=100,title=`dilatation of a circle`
define the parabola with vertex at (0,0) and focus at (0,1/2)
draw⁡p1⁡color=green,style=LINE,thickness=2,p2,p3,p4,style=POINT,color=brown,view=−12..12,0.0..25,numpoints=400,title=`dilatation of a hyperbola`
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