# Difference between revisions of "Lines and Axes"

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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{objects|geometric}} |

− | {{objects|geometric}} | ||

==Lines== | ==Lines== | ||

− | You can enter a line as a linear equation in x and y or in parametric form into the Input Bar. In both cases previously defined variables (e. g. numbers, points, vectors) can be used within the equation. | + | You can enter a line as a linear equation in ''x'' and ''y'' or in parametric form into the Input Bar. In both cases previously defined variables (e.g. numbers, points, vectors) can be used within the equation. |

{{note|You can enter a line’s name at the beginning of the input followed by a colon.}} | {{note|You can enter a line’s name at the beginning of the input followed by a colon.}} | ||

− | {{example|1=<br/> | + | {{example|1= 2D <br/> |

− | * Type in <code>g: 3x + 4y = 2</code> to enter line g as a linear equation. | + | * Type in <code>g: 3x + 4y = 2</code> to enter line ''g'' as a linear equation. |

− | * | + | * You can enter a line in parametric form thus: <code>g: X = (-5, 5) + t (4, -3)</code> |

− | * Define the parameters m = 2 and b = -1. Then, you can enter the equation | + | * Define the parameters ''m'' = 2 and ''b'' = -1. Then, you can enter the equation <code>h: y = m*x + b</code> to get a line ''h'' in y-intercept-form.}} |

+ | |||

+ | |||

+ | {{example|1= 3D <br/> | ||

+ | * You can enter a line in parametric form thus: | ||

+ | ** <code>g: X = (1, 6, 3) + λ (7, -4, 4)</code> ; or via | ||

+ | ** <code>g: Line[(1, 6, 3), Vector[(7, -4, 4)]]</code> | ||

+ | * You can enter a line as an intersection of 2 planes, by one of the following 3 equivalent input : | ||

+ | ** <code>IntersectPath[4x+7y=46,y+z=9]</code><br/> | ||

+ | ** <code>(4x + 7y = 46, y + z = 9)</code><br/> | ||

+ | ** <code>7y = 46 - 4x = 7(9 - z)</code><br/> | ||

+ | }} | ||

+ | |||

==Axes== | ==Axes== | ||

The two coordinate axes are available in commands using the names ''xAxis'' and ''yAxis''. | The two coordinate axes are available in commands using the names ''xAxis'' and ''yAxis''. | ||

{{example|1=The command <code>[[PerpendicularLine Command|PerpendicularLine]][A, xAxis]</code> constructs the perpendicular line to the x-axis through a given point A. }} | {{example|1=The command <code>[[PerpendicularLine Command|PerpendicularLine]][A, xAxis]</code> constructs the perpendicular line to the x-axis through a given point A. }} |

## Latest revision as of 08:11, 13 July 2017

## Lines

You can enter a line as a linear equation in *x* and *y* or in parametric form into the Input Bar. In both cases previously defined variables (e.g. numbers, points, vectors) can be used within the equation.

**Note:**You can enter a line’s name at the beginning of the input followed by a colon.

**Example:**2D

- Type in
`g: 3x + 4y = 2`

to enter line*g*as a linear equation. - You can enter a line in parametric form thus:
`g: X = (-5, 5) + t (4, -3)`

- Define the parameters
*m*= 2 and*b*= -1. Then, you can enter the equation`h: y = m*x + b`

to get a line*h*in y-intercept-form.

**Example:**3D

- You can enter a line in parametric form thus:
`g: X = (1, 6, 3) + λ (7, -4, 4)`

; or via`g: Line[(1, 6, 3), Vector[(7, -4, 4)]]`

- You can enter a line as an intersection of 2 planes, by one of the following 3 equivalent input :
`IntersectPath[4x+7y=46,y+z=9]`

`(4x + 7y = 46, y + z = 9)`

`7y = 46 - 4x = 7(9 - z)`

## Axes

The two coordinate axes are available in commands using the names *xAxis* and *yAxis*.

**Example:**The command

`PerpendicularLine[A, xAxis]`

constructs the perpendicular line to the x-axis through a given point A.## Comments

## Get parameters of a line[edit]

From the line `a: 2.2 x + 3.3 y = 4.4`

you'll get with

`x(a)`

the value 2.2`y(a)`

the value 3.3`z(a)`

the value -4.4 (because GeoGebra save the line equation as`2.2 x + 3.3 y - 4.4 = 0`

.

More informations: Coefficients Command