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Colinear

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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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