line - Maple Help

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

 > $\mathrm{with}\left(\mathrm{geometry}\right):$

define two points $A\left(0,0\right)$ and $B\left(1,1\right)$

 > $\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,1,1\right):$

define the line $l$ that passes through $A$ and $B$

 > $\mathrm{line}\left(l,\left[A,B\right]\right)$
 ${l}$ (1)
 > $\mathrm{form}\left(l\right)$
 ${\mathrm{line2d}}$ (2)
 > $\mathrm{HorizontalName}\left(l\right)$
 ${\mathrm{FAIL}}$ (3)

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

 > $\mathrm{_EnvHorizontalName}≔x:$$\mathrm{_EnvVerticalName}≔y:$
 > $\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,1,1\right):$
 > $\mathrm{line}\left(l,\left[A,B\right]\right)$
 ${l}$ (4)
 > $\mathrm{HorizontalName}\left(l\right)$
 ${x}$ (5)
 > $\mathrm{VerticalName}\left(l\right)$
 ${y}$ (6)
 > $\mathrm{detail}\left(l\right)$
 $\begin{array}{ll}{\text{name of the object}}& {l}\\ {\text{form of the object}}& {\mathrm{line2d}}\\ {\text{equation of the line}}& {-}{x}{+}{y}{=}{0}\end{array}$ (7)

Define a line from its algebraic representation.

 > $\mathrm{line}\left(\mathrm{l2},x-3y\right)$
 ${\mathrm{l2}}$ (8)
 > $\mathrm{Equation}\left(\mathrm{l2}\right)$
 ${x}{-}{3}{}{y}{=}{0}$ (9)