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  2. Distance from a point to a line - Wikipedia

    en.wikipedia.org/.../Distance_from_a_point_to_a_line

    The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite 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. The formula for calculating it can be derived and expressed in several ways.

  3. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    The distance from a point to a line, in the Euclidean plane [7] ... The distance formula itself was first published in 1731 by Alexis Clairaut. [33]

  4. Distance between two parallel lines - Wikipedia

    en.wikipedia.org/wiki/Distance_between_two...

    The distance between two parallel lines in the plane is the minimum distance between any two points. Formula and proof ... Distance from a point to a line; References

  5. Perpendicular distance - Wikipedia

    en.wikipedia.org/wiki/Perpendicular_distance

    The 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 to the line. Likewise, the distance from a point to a curve is measured by a line segment that is perpendicular to a tangent line to the curve at the nearest point on the curve.

  6. Line (geometry) - Wikipedia

    en.wikipedia.org/wiki/Line_(geometry)

    (x 0, y 0, z 0) is any point on the line. a, b, and c are related to the slope of the line, such that the direction vector (a, b, c) is parallel to the line. Parametric equations for lines in higher dimensions are similar in that they are based on the specification of one point on the line and a direction vector.

  7. Mean line segment length - Wikipedia

    en.wikipedia.org/wiki/Mean_line_segment_length

    In geometry, the mean line segment length is the average length of a line segment connecting two points chosen uniformly at random in a given shape. In other words, it is the expected Euclidean distance between two random points, where each point in the shape is equally likely to be chosen.

  8. Line–line intersection - Wikipedia

    en.wikipedia.org/wiki/Lineline_intersection

    In order to find the intersection point of a set of lines, we calculate the point with minimum distance to them. Each line is defined by an origin a i and a unit direction vector n̂ i. The square of the distance from a point p to one of the lines is given from Pythagoras:

  9. Locus (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Locus_(mathematics)

    The set of points equidistant from two intersecting lines is the union of their two angle bisectors. All conic sections are loci: [9] Circle: the set of points at constant distance (the radius) from a fixed point (the center). Parabola: the set of points equidistant from a fixed point (the focus) and a line (the directrix).