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Distance from a point to a line information


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. The algebraic expression for calculating it can be derived and expressed in several ways.

Knowing the 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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Distance from a point to a line

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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...

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Distance from a point to a plane

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the distance from a point to a plane is the distance between a given point and its orthogonal projection on the plane, the perpendicular distance to the...

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Euclidean distance

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computing distances between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been...

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Distance

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distance from the Earth. The same sense of distance is used in Euclidean geometry to define distance from a point to a line, distance from a point to...

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Perpendicular distance

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distance from a point to a line is the distance to the nearest point on that line. That is the point at which a segment from it to the given point is perpendicular...

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Trilinear coordinates

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trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle...

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Distance line

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A distance line, penetration line, cave line, dive reel or guide line is an item of diving equipment used by scuba divers as a means of returning to a...

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Perpendicular

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distance from a point to a line is the distance to the nearest point on that line. That is the point at which a segment from it to the given point is perpendicular...

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Horizon

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the theoretical line to which points on any horizontal plane converge (when projected onto the picture plane) as their distance from the observer increases...

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Basketball court

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on the three-point line that are directly to the left and right of the basket center. The NCAA three-point line is the same distance from the center of...

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Astronomical unit

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Oxford Journals. Archived from the original on 22 October 2012. Retrieved 20 March 2015. The units of length/distance are Å, nm, μm, mm, cm, m, km, au...

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Parabola

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which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus...

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Line segment

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In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between...

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Tangent

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tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz...

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Sum of angles of a triangle

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equidistant (i.e. the distance from each point on one line to the other line is always the same.) Triangle area property: The area of a triangle can be as...

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Hesse normal form

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shortest distance from the origin to the plane. The quadrance (distance squared) from a line a x + b y + c = 0 {\displaystyle ax+by+c=0} to a point ( x ,...

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Antipodal point

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points on a sphere and passing through its center. Given any point on a sphere, its antipodal point is the unique point at greatest distance, whether measured...

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Slope

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the Earth's curvature, if the two points have horizontal distance x1 and x2 from a fixed point, the run is (x2 − x1) = Δx. The slope between the two points...

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Circle

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A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of...

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Pole of inaccessibility

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on the Arctic Ocean pack ice at a distance farthest from any landmass. The original position was wrongly believed to lie at 84°3′N 174°51′W. It is not...

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Spherical coordinate system

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(r, θ, φ): the radial distance of the radial line r connecting the point to the fixed point of origin (which is located on a fixed polar axis, or zenith...

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Equidistant

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Wiktionary, the free dictionary. A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are...

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Distance between two parallel lines

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parallel, the perpendicular distance between them is a constant, so it does not matter which point is chosen to measure the distance. Given the equations of...

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Distance sampling

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based on line transects or point transects. In this method of sampling, the data collected are the distances of the objects being surveyed from these randomly...

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