# Difference between revisions of "PerpendicularLine Command"

From GeoGebra Manual

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− | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} |

− | {{command|geometry}} | + | ;PerpendicularLine( <Point>, <Line> ) |

− | ; PerpendicularLine | + | :Creates a line through the point perpendicular to the given line. |

− | ; PerpendicularLine | + | :{{example|1=<div>Let <code><nowiki>c: -3x + 4y = -6</nowiki></code> be a line and <code><nowiki>A = (-2, -3)</nowiki></code> a point. <code><nowiki>PerpendicularLine(A, c)</nowiki></code> yields the line ''d'': -4''x'' - 3''y'' = 17.</div>}} |

− | ; PerpendicularLine | + | :{{note| 1=For 3D objects a third argument is added to this command to specify the behavior: if 2D view is active, plane <i>z=0</i> is used as third argument, if 3D view is active, <i>space</i> is used instead. See PerpendicularLine( <Point>, <Line>, <Context> ) further below for details.}} |

+ | ;PerpendicularLine( <Point>, <Segment> ) | ||

+ | :Creates a line through the point perpendicular to the given segment. | ||

+ | :{{example|1=<div>Let ''c'' be the segment between the two points ''A'' = (-3, 3) and ''B'' = (0, 1). <code><nowiki>PerpendicularLine(A, c)</nowiki></code> yields the line ''d: -3x + 2y = 15''.</div>}} | ||

+ | ;PerpendicularLine( <Point>, <Vector> ) | ||

+ | :Creates a line through the point perpendicular to the given vector. | ||

+ | :{{example|1=<div>Let <code><nowiki>u = Vector((5, 3), (1, 1))</nowiki></code> and <code><nowiki>A = (-2, 0)</nowiki></code> a point. <code><nowiki>PerpendicularLine(A, u)</nowiki></code> yields the line ''c: 2x + y = -4''.</div>}} | ||

− | {{Note|See also [[ | + | |

− | + | ;PerpendicularLine( <Point>, <Plane> ) | |

− | + | :Creates a perpendicular line to the plane through the given point. | |

− | }} | + | ;PerpendicularLine( <Line> , <Line> ) |

+ | :Creates a perpendicular line to the given lines through the intersection point of the two lines. | ||

+ | ;PerpendicularLine( <Point>, <Direction>, <Direction> ) | ||

+ | :Creates a perpendicular line to the given directions (that can be lines or vectors) through the given point. | ||

+ | ;PerpendicularLine( <Point>, <Line>, <Context> ) | ||

+ | :Creates a perpendicular line to the line through the point and depending on the context. | ||

+ | :*PerpendicularLine( <Point>, <Line>, <Plane> ) creates a perpendicular line to the given line through the point and parallel to the plane. | ||

+ | :*PerpendicularLine( <Point>, <Line>, space ) creates a perpendicular line to the given line through the point. The two lines have an intersection point. This command yields undefined if the point is on the line in 3D. | ||

+ | |||

+ | {{Note|See also [[File:Mode linebisector.svg|link=|22px]] [[Perpendicular Line Tool|Perpendicular Line]] tool.}} |

## Latest revision as of 10:32, 11 October 2017

- PerpendicularLine( <Point>, <Line> )
- Creates a line through the point perpendicular to the given line.
**Example:**Let`c: -3x + 4y = -6`

be a line and`A = (-2, -3)`

a point.`PerpendicularLine(A, c)`

yields the line*d*: -4*x*- 3*y*= 17.

**Note:**For 3D objects a third argument is added to this command to specify the behavior: if 2D view is active, plane*z=0*is used as third argument, if 3D view is active,*space*is used instead. See PerpendicularLine( <Point>, <Line>, <Context> ) further below for details.- PerpendicularLine( <Point>, <Segment> )
- Creates a line through the point perpendicular to the given segment.
**Example:**Let*c*be the segment between the two points*A*= (-3, 3) and*B*= (0, 1).`PerpendicularLine(A, c)`

yields the line*d: -3x + 2y = 15*.

- PerpendicularLine( <Point>, <Vector> )
- Creates a line through the point perpendicular to the given vector.
**Example:**Let`u = Vector((5, 3), (1, 1))`

and`A = (-2, 0)`

a point.`PerpendicularLine(A, u)`

yields the line*c: 2x + y = -4*.

- PerpendicularLine( <Point>, <Plane> )
- Creates a perpendicular line to the plane through the given point.
- PerpendicularLine( <Line> , <Line> )
- Creates a perpendicular line to the given lines through the intersection point of the two lines.
- PerpendicularLine( <Point>, <Direction>, <Direction> )
- Creates a perpendicular line to the given directions (that can be lines or vectors) through the given point.
- PerpendicularLine( <Point>, <Line>, <Context> )
- Creates a perpendicular line to the line through the point and depending on the context.
- PerpendicularLine( <Point>, <Line>, <Plane> ) creates a perpendicular line to the given line through the point and parallel to the plane.
- PerpendicularLine( <Point>, <Line>, space ) creates a perpendicular line to the given line through the point. The two lines have an intersection point. This command yields undefined if the point is on the line in 3D.

**Note:**See also Perpendicular Line tool.