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In Euclidean geometry, the distance from a point to a line is the shortest distance from a given point to any point on an infinite straight line. It is the perpendicular distance of the point to the line, the length of the line segment which joins the point to nearest point on the line.
Learn how to calculate the shortest distance between a point and a line using a formula, a vectorial approach, and examples. See the definition, the proof, and the applications of this concept in geometry and calculus.
Formula of the Distance between Point and Line. The distance [latex]\large{d}[/latex] between the point with coordinates [latex]\large{\left( {{x_0},{y_0}} \right)}[/latex], and the line written in the general form [latex]\large{ax + by + c = 0}[/latex] is calculated as follows.
Learn how to find the shortest distance between a point and a line using the formula d = |Ax 1 + By 1 + C|]/ √ (A 2 + B 2). See solved examples and related topics on distance between two points and lines.
Learn how to calculate the perpendicular distance between a point and a line using dot product and the equation of the line. See examples, formulas, and diagrams.
Learn how to find the distance from a point to a line using slope-intercept form and the Pythagorean Theorem. Watch a video example and see questions and tips from other learners.
Learn how to calculate the distance of a point from a line using the perpendicular distance formula. See the definition, derivation, and solved examples of this geometry concept.
