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What is easiest way to find the a point on a line $(a1, b1)$, $(a2, b2)$ or the extension of the line, which is nearest to a point $(x1, y1)$.

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    Find the point $p$ such that the vector formed between $p$ and $(x_1,y_1)$ is orthogonal to the line.2011-12-26
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    See [this old thread](http://math.stackexchange.com/questions/62633/orthogonal-projection-of-a-point-onto-a-line) for a worked example, which shouldn't be too hard to generalize.2011-12-26

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