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Mathematics-Online lexicon:

Distance Point - Line

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The projection $ X$ of a point $ Q$ on a line through $ P$ with direction $ \vec{u}$ satisfies

$\displaystyle \overrightarrow{PX} = t\vec{u},\quad
t = \frac{(\vec{q}-\vec{p})\cdot\vec{u}}{\vert\vec{u}\vert^2}

From this we obtain the distance of the point $ Q$ from the line by

$\displaystyle d =



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  automatically generated 3/28/2008