# PerpendicularLine Command

From GeoGebra Manual

- 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.