CollinearPoints [{p1,p2,p3,…,pn}]
tests whether the points p1,p2,p3,…,pn are collinear.
CollinearPoints
CollinearPoints [{p1,p2,p3,…,pn}]
tests whether the points p1,p2,p3,…,pn are collinear.
Details
- CollinearPoints is also known as rectilinear.
- Typically used to test whether a set of points lie on the same straight line.
- CollinearPoints [{p1,p2,p3,…,pn}] gives True if the points p3,…,pn are on the line passing through p1 and p2.
- For collinear points p1, p2 and p3, the rank of the matrix {p2-p1,p3-p1} is less than or equal to 1.
Examples
open all close allBasic Examples (2)
The points {0,0},{1,2},{2,4} are collinear:
Plot the points:
Find the equation of the line passing through the points {0,1} and {1,2}:
Scope (4)
CollinearPoints works with two-dimensional points:
Three-dimensional points:
-dimensional points:
CollinearPoints works with numerical coordinates:
Symbolic coordinates:
CollinearPoints over a set of coordinates:
List of points:
Multi-points:
CollinearPoints works for large sets:
Applications (4)
Basic Applications (3)
Find conditions for which two points lie on a line passing through the origin:
Explicit instances:
Find the equation of the line passing through the points {0,1} and {1,2}:
Draw collinear points:
Geometry (1)
Noncollinear points form a polygon:
Collinear points:
Properties & Relations (5)
PositivelyOrientedPoints returns False for collinear points:
NegativelyOrientedPoints returns False for collinear points:
Collinear points are coplanar:
Use RegionMember to test whether points are collinear:
Use InfiniteLine to draw a graphics image:
Related Guides
History
Text
Wolfram Research (2020), CollinearPoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CollinearPoints.html.
CMS
Wolfram Language. 2020. "CollinearPoints." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CollinearPoints.html.
APA
Wolfram Language. (2020). CollinearPoints. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CollinearPoints.html
BibTeX
@misc{reference.wolfram_2025_collinearpoints, author="Wolfram Research", title="{CollinearPoints}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CollinearPoints.html}", note=[Accessed: 09-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_collinearpoints, organization={Wolfram Research}, title={CollinearPoints}, year={2020}, url={https://reference.wolfram.com/language/ref/CollinearPoints.html}, note=[Accessed: 09-January-2026]}