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Point-Line Distance


The point-line distance is the shortest Euclidean distance from a point p to a line. If the line is a+tv with v!=0, then the distance is

 d=||p-a-((p-a)·v)/(v·v)v||.

The subtracted term is the orthogonal projection of p-a onto the direction of the line. Equivalent coordinate formulas are given by the two-dimensional point-line distance and three-dimensional point-line distance.


See also

2-Dimensional Point-Line Distance, 3-Dimensional Point-Line Distance, Point-Plane Distance

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Cite this as:

Weisstein, Eric W. "Point-Line Distance." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Point-LineDistance.html

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