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[[File:vectorpoint-to-line.svg|250px|left|Diagram for vector projection proof]]
Let ''P'' be the point with coordinates (''x''<sub>0</sub>, ''y''<sub>0</sub>) and let the given line have equation ''ax'' + ''by'' + ''c'' = 0. Also, let ''Q'' = (''x''<sub>1</sub>, ''y''<sub>1</sub>) be any point on this line and '''n''' the vector (''a'', ''b'') starting at point ''Q''. The vector '''n''' is perpendicular to the line, and the distance ''d'' from point ''P'' to the line is equal to the length of the orthogonal projection of <math>\overrightarrow{QP}</math> on '''n'''. The length of this projection is given by:
:<math>d = \frac{|\overrightarrow{QP} \cdot \mathbf{n}|}{\| \mathbf{n}\|}.</math>
Now,
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