find the stretch-reflection of a geometric object - Maple 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

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

withgeometry:

Assign the name of the horizontal and vertical axis:

_EnvHorizontalName:=a:_EnvVerticalName:=b:

parabolap,b=a2:

pointA,0,0,linel,b=0:

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

StretchReflectionp1,p,l,A,12:

detailp,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)

drawpstyle=LINE,p1style=POINT

See Also

geometry[dilatation], geometry[draw], geometry[HorizontalName], geometry[objects], geometry[reflection], geometry[transformation], geometry[VerticalName]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam