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 $(x1, y1)$.
Nearest point on the line or its extension from a point
2
$\begingroup$
geometry
-
0Find the point $p$ such that the vector formed between $p$ and $(x_1,y_1)$ is orthogonal to the line. – 2011-12-26
-
0See [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