Distance between two parallel lines: Difference between revisions

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{{Short description|Problem in coordinate geometry}}

{{hatnote|This article considers two lines in a plane. For two lines not in the same plane, see {{slink|Skew lines|Distance}}.}}

{{redirect-distinguish|Distance between two lines|Distance between two skew lines}}

The '''[[distance]] between two [[Parallel (geometry)|parallel]] [[Line (geometry)|lines]]''' in the [[plane (geometry)|plane]] is the minimum distance between any two points.

{{unreferenced|date=April 2013}}

The '''[[distance]] between two [[Line (geometry)|straight lines]]''' in the [[plane (geometry)|plane]] is the minimum distance between any two points lying on the lines. In case of intersecting lines, the distance between them is zero, because the minimum distance between them is zero (at the point of intersection); whereas in case of two [[Parallel (geometry)|parallel]] lines, it is the [[perpendicular]] distance from a [[Point (geometry)|point]] on one line to the other line.

== Formula and proof ==

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:<math>y = -x/m \, .</math>

This distance can be found by first solving the [[linear systems]]

:<math>\begin{cases}

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==See also==

*[[Distance from a point to a line]]

*[[Skew lines#Distance]]

==References==

*''Abstand'' In: ''Schülerduden – Mathematik II''. Bibliographisches Institut & F. A. Brockhaus, 2004, {{ISBN|3-411-04275-3}}, pp. 17-19 (German)

*Hardt Krämer, Rolf Höwelmann, Ingo Klemisch: ''Analytische Geometrie und Lineare Akgebra''. Diesterweg, 1988, {{ISBN|3-425-05301-9}}, p. 298 (German)

==External links ==

*Florian Modler: [http://www.emath.de/Referate/Zusammenfassung-wichtiger-Formeln.pdf ''Vektorprodukte, Abstandsaufgaben, Lagebeziehungen, Winkelberechnung – Wann welche Formel?''], pp. 44-59 (German)

*A. J. Hobson: [https://archive.uea.ac.uk/jtm/8/Lec8p5.pdf ''“JUST THE MATHS” - UNIT NUMBER 8.5 - VECTORS 5 (Vector equations of straight lines)''], pp. 8-9

[[Category:Euclidean geometry]]

*[[Skew lines#Category:Distance]]