WOLFRAM

Wolfram Language & System Documentation Center

Midpoint[{p1,p2}]

gives the midpoint of the line segment connecting the points p1 and p2.

Midpoint[Line[{p1,p2}]]

gives the midpoint of a line.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Properties & Relations  
Possible Issues  
See Also
Related Guides
History
Cite this Page

Midpoint

Midpoint[{p1,p2}]

gives the midpoint of the line segment connecting the points p1 and p2.

Midpoint[Line[{p1,p2}]]

gives the midpoint of a line.

Details

Examples

open all close all

Basic Examples  (1)

Find the midpoint of two points:

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

With explicit Point objects, the output is also a Point object:

Wolfram Language code: Midpoint[{Point[{1, 1}], Point[{2, 3}]}]

Scope  (5)

Midpoint works in 2D:

Wolfram Language code: Midpoint[{{1, 1}, {3, 4}}]

Midpoint works in 3D:

Wolfram Language code: Midpoint[{{1, 2, 3}, {4, 5, 6}}]

Midpoint works in nD:

Wolfram Language code: Midpoint[{{1, 2, -1, 3}, {4, 2, -3, -2}}]

Midpoint works on Point:

Wolfram Language code: Midpoint[{Point[{1, 2}], Point[{-2, 3}]}]

Midpoint works on symbolic coordinates:

Wolfram Language code: Midpoint[{{a, b}, {c, d}}]

Properties & Relations  (4)

The midpoint is equidistant from the two points:

Wolfram Language code: EuclideanDistance[{1, 2}, Midpoint[{{1, 2}, {3, 4}}]]
Wolfram Language code: EuclideanDistance[Midpoint[{{1, 2}, {3, 4}}], {3, 4}]

For coordinates, Midpoint gives the same result as Mean:

Wolfram Language code: Midpoint[{{1, 2}, {-3, 5}}]
Wolfram Language code: Mean[{{1, 2}, {-3, 5}}]

The PerpendicularBisector passes through the Midpoint:

Wolfram Language code: PerpendicularBisector[{{1, 2}, {-3, 5}}]
Wolfram Language code: Midpoint[{{1, 2}, {-3, 5}}]
Wolfram Language code: Graphics[{Point[{-1, 7 / 2}], Line[{{1, 2}, {-3, 5}}], Style[InfiniteLine[{-1, 7 / 2}, {3, 4}], Dashed]}]

TriangleCenter[{a,b,c},"Midpoint"] is equivalent to Midpoint[{a,c}]:

Wolfram Language code: TriangleCenter[{{0, 0}, {1, 0}, {1, 3}}, "Midpoint"]
Wolfram Language code: Midpoint[{{0, 0}, {1, 3}}]

Possible Issues  (2)

Midpoint behaves differently on symbolic points than Mean:

Wolfram Language code: Midpoint[{a, b}]
Wolfram Language code: Mean[{a, b}]

Midpoint behaves differently on Point objects than Mean:

Wolfram Language code: Midpoint[{Point[{-1, 2}], Point[{3, -2}]}]
Wolfram Language code: Mean[{Point[{-1, 2}], Point[{3, -2}]}]
Wolfram Research (2019), Midpoint, Wolfram Language function, https://reference.wolfram.com/language/ref/Midpoint.html.

Text

Wolfram Research (2019), Midpoint, Wolfram Language function, https://reference.wolfram.com/language/ref/Midpoint.html.

CMS

Wolfram Language. 2019. "Midpoint." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Midpoint.html.

APA

Wolfram Language. (2019). Midpoint. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Midpoint.html

BibTeX

@misc{reference.wolfram_2026_midpoint, author="Wolfram Research", title="{Midpoint}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/Midpoint.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_midpoint, organization={Wolfram Research}, title={Midpoint}, year={2019}, url={https://reference.wolfram.com/language/ref/Midpoint.html}, note=[Accessed: 13-June-2026]}