Distance Between Point and Line

Distance from a Point to a Line is the length of the shortest segment from a given point to a given line.

The distance (or perpendicular distance) from a point to a line is the shortest distance from a point to a line in Euclidean geometry *. It is the length of the line segment which joins the point to the line and is perpendicular to the line.

Knowing the shortest distance from a point to a line can be useful in various situations—for example, finding the shortest distance to reach a road, quantifying the scatter on a graph, etc. In Deming regression, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in orthogonal regression in which the degree of imperfection of the fit is measured for each data point as the perpendicular distance of the point from the regression line.

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* Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid’s method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these.

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