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Mathematics-Online lexicon:

Translation of a Cartesian Coordinate System

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Moving the origin $ O$ to

$\displaystyle O' = (p_1,p_2,p_3), $

without changing the directions of the axes, the coordinates change as follows:

$\displaystyle X' = (x_1-p_1,x_2-p_2,x_3-p_3)\, $

\includegraphics[width=.6\linewidth]{a_translation.eps}
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  automatically generated 3/28/2008