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== | ||
+ | *[[Parallel]] | ||
+ | *[[Skew]] | ||
+ | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
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Latest revision as of 15:33, 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 .