Collinear Points Checker

About this calculator

Three points are collinear when they all lie on the same straight line. The standard test computes the signed area of the triangle they would form: for points (x₁,y₁), (x₂,y₂), (x₃,y₃), the expression x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂) equals zero exactly when the triangle collapses to a line — an equivalent way to say the slope between the first two points matches the slope between the last two.

This check matters in computational geometry and computer graphics, where a triangle with zero area is a degenerate triangle that breaks mesh rendering and collision detection algorithms. GIS software uses it to simplify routes and detect redundant vertices in a polyline, and structural engineers use the same logic to confirm that support points or survey markers actually align rather than deviating by a small but real amount.

Enter the three coordinate pairs and the calculator evaluates the signed-area formula for you, telling you directly whether the points fall on one line.