Difference between revisions of "PerpendicularLine Command"
From GeoGebra Manual
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: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 ''c'': -3''x'' + 4''y'' = -6 be a line and ''A'' = (-2, -3) a point. <code><nowiki>PerpendicularLine[ A, c ]</nowiki></code> yields the line ''d'': -4''x'' - 3''y'' = 17.</div>}} | :{{example|1=<div>Let ''c'': -3''x'' + 4''y'' = -6 be a line and ''A'' = (-2, -3) 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> ] for details.}} | ||
;PerpendicularLine[ <Point>, <Segment> ] | ;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. | ||
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:{{example|1=<div>Let ''u'' be a vector between two points: ''u'' = ''Vector''[ (5, 3), (1, 1) ] and A = (-2, 0) a point. <code><nowiki>PerpendicularLine[ A, u ]</nowiki></code> yields the line ''c: 2x + y = -4''.</div>}} | :{{example|1=<div>Let ''u'' be a vector between two points: ''u'' = ''Vector''[ (5, 3), (1, 1) ] and A = (-2, 0) a point. <code><nowiki>PerpendicularLine[ A, u ]</nowiki></code> yields the line ''c: 2x + y = -4''.</div>}} | ||
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;PerpendicularLine[ <Point>, <Plane> ] | ;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. | ||
Revision as of 13:41, 29 July 2015
- 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: -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> ] 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 be a vector between two points: 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.
Perpendicular Line tool.
