condition of orthogonalityConditionOfOrthogonality2004-11-07 10:06:032005-02-19 12:55:21Resultorthogonalopposite inversestraight lineslope% this is the default PlanetMath preamble. as your knowledge
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\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}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 {\em opposite inverses} of each other, i.e. \PMlinkname{iff}{Biconditional}
\[m_1m_2 = -1.\]
\textbf{Example.} \,The lines \,$y = (1+\sqrt{2})x$\, and \,$y = (1-\sqrt{2})x$\, are at right angles to each other.
\begin{center}
\includegraphics{orthogon}
\end{center}