geometry - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Geometry : 2-D Euclidean : Transformations : geometry/StretchReflection

geometry

  

StretchReflection

  

find the stretch-reflection of a geometric object

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

StretchReflection(Q, P, l, O, k )

Parameters

Q

-

the name of the object to be created

P

-

geometric object

l

-

line

O

-

point on l

k

-

number which is the ratio of the stretch-reflection

Description

• 

Let l be a fixed line of the plane and O a fixed point on l, and let k be a given nonzero real number. By the stretch-reflection SO,k,l we mean the product RlHO,k where Rl is the reflection with respect to line l, and HO,k is the dilatation with center O and ratio k. The line l is called the axis of the stretch-reflection, the point O is called the center of the stretch-reflection, and k is called the ratio of the stretch-reflection

• 

For a detailed description of Q (the object created), use the routine detail (i.e., detail(Q))

• 

The command with(geometry,StretchReflection) allows the use of the abbreviated form of this command.

Examples

with(geometry):

Assign the name of the horizontal and vertical axis:

_EnvHorizontalName := a: _EnvVerticalName := b:

parabola(p,b=a^2):

point(A,0,0), line(l,b=0):

dilate p with center A and ratio 1/2, then reflect this object with respect to the line l

StretchReflection(p1,p,l,A,1/2):

detail({p,p1});

name of the objectpform of the objectparabola2dvertex0,0focus0,14directrixb+14=0equation of the parabolaa2+b=0,name of the objectp1form of the objectparabola2dvertex0,0focus0,18directrix2b+14=0equation of the parabola4a22b=0

(1)

draw({p(style=LINE),p1(style=POINT)});

See Also

geometry[dilatation]

geometry[draw]

geometry[HorizontalName]

geometry[objects]

geometry[reflection]

geometry[transformation]

geometry[VerticalName]