CoplanarPoints [{p1,p2,p3,p4,…,pn}]
tests whether the points p1,p2,p3,p4,…,pn are coplanar.
CoplanarPoints
CoplanarPoints [{p1,p2,p3,p4,…,pn}]
tests whether the points p1,p2,p3,p4,…,pn 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,…,pn}] gives True if the points p4,…,pn 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.
Examples
open all close allBasic 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}:
Scope (4)
CoplanarPoints works with two-dimensional points:
Three-dimensional points:
n-dimensional points:
CoplanarPoints works with numerical coordinates:
Symbolic coordinates:
CoplanarPoints over a set of coordinates:
List of points:
Multi-points:
CoplanarPoints works for large sets:
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)
PositivelyOrientedPoints returns False for coplanar points:
NegativelyOrientedPoints returns False for coplanar points:
Collinear points are coplanar:
Use RegionMember to test whether points are coplanar:
Use InfinitePlane to draw a graphics image:
Related Guides
History
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.html
BibTeX
@misc{reference.wolfram_2025_coplanarpoints, author="Wolfram Research", title="{CoplanarPoints}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CoplanarPoints.html}", note=[Accessed: 12-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_coplanarpoints, organization={Wolfram Research}, title={CoplanarPoints}, year={2020}, url={https://reference.wolfram.com/language/ref/CoplanarPoints.html}, note=[Accessed: 12-January-2026]}