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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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