Distance from a point to a line

<p>The distance (or perpendicular distance) from a point to a line is the shortest <a href="/facts/Euclidean_distance/9qDoQKQe">distance</a> from a fixed <a href="/facts/Point_(geometry)/6YPAvX2a">point</a> to any point on a fixed infinite <a href="/facts/Line_(mathematics)/gJqsr4Gj">line</a> in <a href="/facts/Euclidean_geometry/V6cTcoCy">Euclidean geometry</a>. It is the length of the <a href="/facts/Line_segment/V8E0M4qk">line segment</a> which joins the point to the line and is <a href="/facts/Perpendicular/u0k8xqx4">perpendicular</a> to the line. The formula for calculating it can be derived and expressed in several ways.
</p><p>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 <a href="/facts/Deming_regression/j4bFDpub">Deming regression</a>, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in <a href="/facts/Orthogonal_regression/j4bFDpub">orthogonal regression</a> 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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Distance from a point to a line open-in-new

Distance from a point to a line