geometry
rotation
find the rotation of a geometric object with respect to a given point
Calling Sequence
Parameters
Description
Examples
rotation(Q, P, g, co, R)
Q
-
the name of the object to be created
P
geometric object
g
the angle of rotation
co
the direction of rotation, either clockwise or counterclockwise
R
(optional) the center of rotation
Let R be a fixed point of the plane, g and co denote the sensed angle. By the rotation RO,g,co we mean the transformation of the plane S onto itself which carries each point P of the plane into the point P1 of the plane such that OP1 = OP and the angle POP1=g in the direction specified by co.
Point O is called the center of the rotation, and g is called the angle of the rotation.
If the fifth argument is omitted, then the origin is the center of rotation.
For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
The command with(geometry,rotation) allows the use of the abbreviated form of this command.
withgeometry:
pointP,2,0,pointQ,1,0
P,Q
rotationP1,P,π,counterclockwise
P1
coordinatesP1
−2,0
rotationP2,P,π2,clockwise,Q
P2
coordinatesP2
1,−1
f≔y2=x:parabolap,f,x,y:
pointOO,0,0:
rotationp1,p,π2,counterclockwise,OO:
detailp,p1
name of the objectpform of the objectparabola2dvertex0,0focus14,0directrixx+14=0equation of the parabolay2−x=0,name of the objectp1form of the objectparabola2dvertex0,0focus0,14directrixy+14=0equation of the parabolax2−y=0
rotationp2,p,π,counterclockwise,OO:
rotationp3,p,π2,clockwise,OO:
drawpstyle=LINE,thickness=2,p1,p2,p3,style=POINT,symbol=DIAMOND,color=green,title=`rotation of a parabola`
See Also
geometry/objects
geometry/transformation
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