geometry
reflection
find the reflection of a geometric object with respect to a given point or line
Calling Sequence
Parameters
Description
Examples
reflection(Q, P, c)
Q
-
the name of the object to be created
P
geometric object
c
point or line
Let c be a fixed point in the plane. By the reflection (or half-turn) Rc in point c 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 c is the midpoint of PQ. Point c is called the center of the reflection.
Let c be a fixed line in the plane. By the reflection Rc about line c 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 c goes through the midpoint of PQ and is perpendicular to PQ.
For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))
The command with(geometry,reflection) allows the use of the abbreviated form of this command.
withgeometry:
reflection of a point with respect to a line
pointP,2,3,linel,a+b=1,a,b
P,l
reflectionQ,P,l
coordinatesQ
−2,−1
reflection of a line with respect to a line
linex_axis,y=0,x,y:
reflectionl1,l,x_axis:
drawl,l1
reflection of a circle with respect to a line
circlec,pointOO,0,0,1:
detailc
assume that the names of the horizontal and vertical axes are _x and _y, respectively
name of the objectcform of the objectcircle2dname of the centerOOcoordinates of the center0,0radius of the circle1equation of the circle_x2+_y2−1=0
linel1,pointa1,1,0,pointa2,0,1:
linel2,pointb1,−1,0,pointb2,0,1:
linel3,pointc1,−1,0,pointc2,0,−1:
linel4,pointd1,0,−1,pointd2,1,0:
reflectionc1,c,l1:reflectionc2,c,l2:
reflectionc3,c,l3:reflectionc4,c,l4:
drawc1,c2,c3,c4,ccolor=orange,color=blue,axes=BOX,style=POINT,symbol=DIAMOND
See Also
geometry/objects
geometry/transformation
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