PerpendicularBisector [{p1,p2}]
gives the perpendicular bisector of the line segment connecting p1 and p2.
PerpendicularBisector [Line[{p1,p2}]]
gives the perpendicular bisector of a line segment.
PerpendicularBisector
PerpendicularBisector [{p1,p2}]
gives the perpendicular bisector of the line segment connecting p1 and p2.
PerpendicularBisector [Line[{p1,p2}]]
gives the perpendicular bisector of a line segment.
Details
- PerpendicularBisector gives an InfiniteLine object.
- The pi in PerpendicularBisector [{p1,p2}] can be lists of coordinates or explicit Point objects.
- PerpendicularBisector [Line [{p1,p2}]] is equivalent to PerpendicularBisector [{p1,p2}].
- PerpendicularBisector gives the line that divides the line segment into two equal segments and that intersects the segment at right angles.
- PerpendicularBisector only works in 2D.
- PerpendicularBisector can be used with symbolic points in GeometricScene .
Examples
open all close allBasic Examples (2)
Calculate the perpendicular bisector of a line segment:
Calculate the perpendicular bisector of two points:
Scope (3)
Calculate the perpendicular bisector of a line segment containing (0, 0) and (1, 0):
Visualize:
Calculate the perpendicular bisector of the line segment from (0, 0) to (1, 1):
Visualize:
Calculate the perpendicular bisector of an abstract line:
Properties & Relations (2)
The PerpendicularBisector is perpendicular to the line segment and passes through the Midpoint :
TriangleConstruct [{a,b,c},"PerpendicularBisector"] is equivalent to PerpendicularBisector [{a,c}]:
Possible Issues (1)
PerpendicularBisector only works in 2D:
Neat Examples (1)
The three perpendicular bisectors of a triangle meet at the triangle's circumcenter:
Related Guides
History
Text
Wolfram Research (2019), PerpendicularBisector, Wolfram Language function, https://reference.wolfram.com/language/ref/PerpendicularBisector.html.
CMS
Wolfram Language. 2019. "PerpendicularBisector." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PerpendicularBisector.html.
APA
Wolfram Language. (2019). PerpendicularBisector. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PerpendicularBisector.html
BibTeX
@misc{reference.wolfram_2025_perpendicularbisector, author="Wolfram Research", title="{PerpendicularBisector}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PerpendicularBisector.html}", note=[Accessed: 10-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_perpendicularbisector, organization={Wolfram Research}, title={PerpendicularBisector}, year={2019}, url={https://reference.wolfram.com/language/ref/PerpendicularBisector.html}, note=[Accessed: 10-January-2026]}