# Difference between revisions of "Perpendicular"

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==Definition== | ==Definition== | ||

− | Two [[line]]s <math>l</math> and <math>m</math> are said to be '''perpendicular''' if they intersect in [[right angle]]s. We denote this relationship by <math>l \perp m</math>. | + | Two [[line]]s <math>l</math> and <math>m</math> are said to be '''perpendicular''' if they intersect in [[right angle]]s. We denote this relationship by <math>l \perp m</math>. |

===For non-linear objects=== | ===For non-linear objects=== | ||

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==Coordinate Plane== | ==Coordinate Plane== | ||

− | Two linear graphs in the Cartesian coordinate plane are perpendicular if and only if one's slope is the negative reciprocal of the other's. This means that their slopes must have a product of <math>-1</math>. | + | Two linear graphs in the Cartesian coordinate plane are perpendicular if and only if one's [[slope]] is the negative reciprocal of the other's. This means that their slopes must have a product of <math>-1</math>. |

==See Also== | ==See Also== | ||

*[[Parallel]] | *[[Parallel]] | ||

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*[[Skew]] | *[[Skew]] | ||

+ | [[Category:Definition]] | ||

[[Category:Geometry]] | [[Category:Geometry]] | ||

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## Latest revision as of 14:33, 20 October 2007

Being **perpendicular** is a property of lines in a plane. Generally, when the term is used, it refers to the definition of perpendicular in Euclidean geometry.

## Definition

Two lines and are said to be **perpendicular** if they intersect in right angles. We denote this relationship by .

### For non-linear objects

One can also discuss perpendicularity of other objects. If a line intersects a plane at a point , we say that if and only if for *every* line in passing through , .

If a plane intersects another plane in a line , we say that if and only if: for line and passing through , and implies .

## Coordinate Plane

Two linear graphs in the Cartesian coordinate plane are perpendicular if and only if one's slope is the negative reciprocal of the other's. This means that their slopes must have a product of .