# 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

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## Basic 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:

Wolfram Research (2020), CollinearPoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CollinearPoints.html.

#### 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_2022_collinearpoints, author="Wolfram Research", title="{CollinearPoints}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CollinearPoints.html}", note=[Accessed: 31-May-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_collinearpoints, organization={Wolfram Research}, title={CollinearPoints}, year={2020}, url={https://reference.wolfram.com/language/ref/CollinearPoints.html}, note=[Accessed: 31-May-2023 ]}