define a line - Maple Help

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geometry[line] - define a line

Calling Sequence

line(l, [A, B])

line(l, eqn, n)

Parameters

l

-

the name of the line

A, B

-

two points

eqn

-

the algebraic representation of a line, that is, a polynomial or equation

n

-

(optional) a list of two names representing the names of the horizontal-axis and vertical-axis

Description

• 

In the geometry package, a line means a ``straight line''. It is unlimited in extent, i.e., it may be extended in either direction indefinitely.

• 

A line l can be defined as follows:

– 

from two given points A and B

– 

from its algebraic representation eqn. I.e., eqn is a polynomial or an equation. If the third optional argument is not given, then:

– 

if names are assigned to the two environment variables _EnvHorizontalName and _EnvVerticalName, then these two names will be used as the names of the horizontal-axis and vertical-axis respectively.

– 

otherwise, Maple will prompt the user to input the names of the axes.

• 

To access the information relating to a line l, use the following function calls:

form(l)

returns the form of the geometric object (i.e., line2d if l is a line).

Equation(l)

returns the equation that represents the line l.

HorizontalName(l)

returns the name of the horizontal-axis; or FAIL if the axis is not assigned a name.

VerticalName(l)

returns the name of the vertical-axis; or FAIL if the axis is not assigned a name.

detail(l)

returns a detailed description of the line l.

• 

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

Examples

withgeometry:

define two points A0,0 and B1,1

pointA,0,0,pointB,1,1:

define the line l that passes through A and B

linel,A,B

l

(1)

forml

line2d

(2)

HorizontalNamel

FAIL

(3)

To assign names to the axes, assign the names to the environment variables _EnvHorizontalName and _EnvVerticalName.

_EnvHorizontalName:=x:_EnvVerticalName:=y:

pointA,0,0,pointB,1,1:

linel,A,B

l

(4)

HorizontalNamel

x

(5)

VerticalNamel

y

(6)

detaill

name of the objectlform of the objectline2dequation of the linex+y=0

(7)

Define a line from its algebraic representation.

linel2,x3y

l2

(8)

Equationl2

x3y=0

(9)

See Also

geometry[AreConcurrent], geometry[AreParallel], geometry[ArePerpendicular], geometry[AreTangent], geometry[distance], geometry[FindAngle], geometry[HorizontalName], geometry[intersection], geometry[IsOnLine], geometry[objects], geometry[ParallelLine], geometry[PerpenBisector], geometry[PerpendicularLine], geometry[Polar], geometry[Pole], geometry[projection], geometry[randpoint], geometry[slope], geometry[transformation], geometry[VerticalName]


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