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InfiniteLineThrough[{p1,p2,…}]

gives an infinite line passing through the points pi.

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Basic Examples  
Scope  
Applications  
Basic Applications  
Properties & Relations  
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InfiniteLineThrough

InfiniteLineThrough[{p1,p2,…}]

gives an infinite line passing through the points pi.

Details

Examples

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Basic Examples  (2)

An infinite line passing through three points:

Wolfram Language code: pts = {{0, 0}, {1, 1}, {2, 2}};
Wolfram Language code: InfiniteLineThrough[pts]

Display the line:

Wolfram Language code: Graphics[{%, Red, Point[pts]}]

RegionDistance from an infinite line to a point:

Wolfram Language code: RegionDistance[InfiniteLineThrough[{{0, 0}, {1, 2}}], {5, 6}]

Scope  (2)

InfiniteLineThrough works on coordinates:

Wolfram Language code: InfiniteLineThrough[{{0, 0}, {2, 2}, {4, 4}}]

Multiple points:

Wolfram Language code: InfiniteLineThrough[{Point[{0, 0}], Point[{1, 0}]}]

Collections of points:

Wolfram Language code: InfiniteLineThrough[Point[{{0, 0}, {1, 0}}]]

InfiniteLineThrough works with points in 1D:

Wolfram Language code: InfiniteLineThrough[{{0}, {2}}]

2D:

Wolfram Language code: InfiniteLineThrough[{{0, 0}, {2, 2}}]

D:

Wolfram Language code: InfiniteLineThrough[{{0, 0, 1, 0}, {2, 2, 3, 0}}]

Applications  (3)

Basic Applications  (3)

Visualize the line passing through three points:

Wolfram Language code: pts = {{0, 0}, {1, 1}, {2, 2}};
Wolfram Language code: Graphics[{InfiniteLineThrough[pts], Red, Point[pts]}]

Find the implicit representation of the circle passing through three points:

Wolfram Language code: RegionConvert[InfiniteLineThrough[{{1, 0}, {3, -1}}], "Implicit"]

Its parametric representation:

Wolfram Language code: RegionConvert[InfiniteLineThrough[{{1, 0}, {3, -1}}], "Parametric"]

Find an InfiniteLine that best fits a set of points:

Wolfram Language code: pts = Sort @ {{-24, -20}, {-24, -19}, {-25, -20}, {-80, -59}, {-76, -56}, {-95, -70}, {-83, -61}, {-46, -35}, {-58, -44}};
Wolfram Language code: lines = InfiniteLineThrough /@ Subsets[pts, {2}];
Wolfram Language code: TakeSmallestBy[lines, Count[RegionMember[#, pts], False]&, 1]

Best fit using RegionFit:

Wolfram Language code: RegionFit[pts, "Line"]

Compare:

Wolfram Language code: Graphics[{Point[pts], %, Red, First[%%]}]

Properties & Relations  (2)

InfiniteLineThrough returns an InfiniteLine object:

Wolfram Language code: InfiniteLineThrough[{{0, 0}, {2, 2}, {4, 4}}]

Use RegionFit to obtain an InfiniteLine that best fits a set of points:

Wolfram Language code: RegionFit[{{-24, -20}, {-24, -19}, {-25, -20}, {-80, -59}, {-76, -56}}, "Line"]
Wolfram Research (2022), InfiniteLineThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/InfiniteLineThrough.html.

Text

Wolfram Research (2022), InfiniteLineThrough, Wolfram Language function, https://reference.wolfram.com/language/ref/InfiniteLineThrough.html.

CMS

Wolfram Language. 2022. "InfiniteLineThrough." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InfiniteLineThrough.html.

APA

Wolfram Language. (2022). InfiniteLineThrough. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InfiniteLineThrough.html

BibTeX

@misc{reference.wolfram_2026_infinitelinethrough, author="Wolfram Research", title="{InfiniteLineThrough}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/InfiniteLineThrough.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_infinitelinethrough, organization={Wolfram Research}, title={InfiniteLineThrough}, year={2022}, url={https://reference.wolfram.com/language/ref/InfiniteLineThrough.html}, note=[Accessed: 13-June-2026]}