PerpendicularLine Command

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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> ] 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 Mode linebisector.svg Perpendicular Line tool.
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