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Collinear Points

Illustration

Illustration

Alternate name
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.

Educational grade level

high school level

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