Difference between revisions of "PerpendicularLine Command"
From GeoGebra Manual
m |
m (Text replace - ";(.*)\[(.*)\]" to ";$1($2)") |
||
Line 1: | Line 1: | ||
<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|geometry}} | ||
− | ;PerpendicularLine | + | ;PerpendicularLine( <Point>, <Line> ) |
:Creates a line through the point perpendicular to the given line. | :Creates a line through the point perpendicular to the given line. | ||
:{{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>}} | :{{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>}} | ||
:{{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.}} | :{{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 | + | ;PerpendicularLine( <Point>, <Segment> ) |
:Creates a line through the point perpendicular to the given 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>}} | :{{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 | + | ;PerpendicularLine( <Point>, <Vector> ) |
:Creates a line through the point perpendicular to the given 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>}} | :{{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>}} | ||
− | ;PerpendicularLine | + | ;PerpendicularLine( <Point>, <Plane> ) |
:Creates a perpendicular line to the plane through the given point. | :Creates a perpendicular line to the plane through the given point. | ||
− | ;PerpendicularLine | + | ;PerpendicularLine( <Line> , <Line> ) |
:Creates a perpendicular line to the given lines through the intersection point of the two lines. | :Creates a perpendicular line to the given lines through the intersection point of the two lines. | ||
− | ;PerpendicularLine | + | ;PerpendicularLine( <Point>, <Direction>, <Direction> ) |
:Creates a perpendicular line to the given directions (that can be lines or vectors) through the given point. | :Creates a perpendicular line to the given directions (that can be lines or vectors) through the given point. | ||
− | ;PerpendicularLine | + | ;PerpendicularLine( <Point>, <Line>, <Context> ) |
:Creates a perpendicular line to the line through the point and depending on the 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>, <Plane> ] creates a perpendicular line to the given line through the point and parallel to the plane. |
Revision as of 17:17, 7 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 andA = (-2, -3)
a point.PerpendicularLine[ A, c ]
yields the line d: -4x - 3y = 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) ]
andA = (-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.