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geometry

  

rotation

  

find the rotation of a geometric object with respect to a given point

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

rotation(Q, P, g, co, R)

Parameters

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

Description

• 

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 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.

Examples

withgeometry:

pointP,2,0,pointQ,1,0

P,Q

(1)

rotationP1,P,π,'counterclockwise'

P1

(2)

coordinatesP1

2,0

(3)

rotationP2,P,π2,'clockwise',Q

P2

(4)

coordinatesP2

1,1

(5)

fy2=x:parabolap,f,x,y:

pointOO,0,0:

rotationp1,p,π2,'counterclockwise',OO:

detailp1,p

name of the objectpform of the objectparabola2dvertex0,0focus14,0directrixx+14=0equation of the parabolay2x=0,name of the objectp1form of the objectparabola2dvertex0,0focus0,14directrixy+14=0equation of the parabolax2y=0

(6)

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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