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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.
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 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.
Learn how to calculate the perpendicular distance from a point to 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 shortest distance from a point to a line using the formula d = A2 +B2∣Am +Bn+ C. See proof, examples and diagrams of the construction.
Learn how to calculate the distance between a point and a line using the formula and the perpendicular distance. See solved examples and practice problems on this geometry topic.
