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    Collinear Points

    Illustration

    Illustration

    Alternate name

    colinear

    Basic definition

    Three or more points are said to be collinear if they lie on the same straight line.

    Detailed definition

    Three or more points P_1, P_2, P_3, ..., are said to be collinear if they lie on a single straight line L. A line on which points lie, especially if it is related to a geometric figure such as a triangle, is sometimes called an axis. Two points are trivially collinear since two points determine a line. Three points x_i = (x_i, y_i, z_i) for i = 1, 2, 3 are collinear iff the ratios of distances satisfy x_2 - x_1 :y_2 - y_1 :z_2 - z_1 = x_3 - x_1 :y_3 - y_1 :z_3 - z_1.

    Related terms

    axis | concyclic | configuration | directed angle | Droz-Farny theorem | general position | line | N-cluster | point-line distance--3-dimensional | Sylvester's line problem

    Educational grade level

    high school level

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