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CoplanarPoints—Wolfram Language Documentation

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BUILT-IN SYMBOL

CoplanarPoints[{p₁,p₂,p₃,p₄,…,p_n}]

tests whether the points p₁,p₂,p₃,p₄,…,p_n are coplanar.

Details

CoplanarPoints is also known as linearly dependent.
Typically used to test whether a set of points lie on the same plane.
CoplanarPoints[{p₁,p₂,p₃,p₄,…,p_n}] gives True if the points p₄,…,p_n are on the plane passing through the points p₁, p₂ and p₃.
For coplanar points p₁, p₂, p₃ and p₄, the rank of the matrix {p₂-p₁,p₃-p₁,p₄-p₁} is less than or equal to 2.

Examplesopen allclose all Basic Examples (2)

The points {0,0,0}, {1,1,-2}, {-1,2,-1}, {3,-4,1} are coplanar:

Plot the points:

Find the equation of the plane containing the points {0,0,0}, {1,1,-2} and {-1,2,-1}:

Applications (5) Basic Applications (4)

Find conditions for which two points lie on a plane passing through the origin:

Explicit instances:

2D points lie on the same plane:

Find the equation of a plane containing a set of points:

Draw coplanar points:

Geometry (1)

A face of a polyhedron lies on a plane:

Properties & Relations (5) Wolfram Research (2020), CoplanarPoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CoplanarPoints.html. Text Wolfram Research (2020), CoplanarPoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CoplanarPoints.html.CMS Wolfram Language. 2020. "CoplanarPoints." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoplanarPoints.html.APA Wolfram Language. (2020). CoplanarPoints. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoplanarPoints.htmlBibTeX @misc{reference.wolfram_2025_coplanarpoints, author="Wolfram Research", title="{CoplanarPoints}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CoplanarPoints.html}", note=[Accessed: 11-July-2025 ]}BibLaTeX @online{reference.wolfram_2025_coplanarpoints, organization={Wolfram Research}, title={CoplanarPoints}, year={2020}, url={https://reference.wolfram.com/language/ref/CoplanarPoints.html}, note=[Accessed: 11-July-2025 ]}

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