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[parent] condition of orthogonality (Result)

Let two straight lines of the $ xy$-plane have the slopes $ m_1$ and $ m_2$. The lines are at right angles to each other iff $ m_1$ and $ m_2$ are the opposite inverses of each other, i.e. iff

$\displaystyle m_1m_2 = -1.$

Example. The lines $ y = (1+\sqrt{2})x$ and $ y = (1-\sqrt{2})x$ are at right angles to each other.

\includegraphics{orthogon}



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See Also: orthogonal curve, inverse number, opposite number, normal line, angle between two lines, perpendicularity in Euclidean plane, evolute, example of finding catacaustic

Other names:  condition of perpendicularity
Also defines:  opposite inverse
Keywords:  straight line, slope

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Cross-references: iff, right angles, slopes, lines, straight
There are 8 references to this entry.

This is version 11 of condition of orthogonality, born on 2004-11-07, modified 2005-02-19.
Object id is 6455, canonical name is ConditionOfOrthogonality.
Accessed 6371 times total.

Classification:
AMS MSC: 15A57 (Linear and multilinear algebra; matrix theory :: Other types of matrices )
 51F20 (Geometry :: Metric geometry :: Congruence and orthogonality)
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