Distance Formula
Pronunciation: /ˈdɪst.əns ˈfɔɹ.mjə.lə/ Explain
Click on the blue points and drag them to change the figure.
The distance formula is the square root of the square of the difference in x plus the square of the difference in y.
 Manipulative 1  Distance formula Created with GeoGebra. 

The distance formula is used to calculate the
distance
between any two points.^{[2]} For the distance between the origin
and a point in a plane, the formula is
where the coordinate of the point is
The formula for the
distance between any two points on the Cartesian plane is
The distance formula is derived from the Pythagorean theorem which states for a
right triangle with legs of length A and
B, and an hypotenuse of length C,
then the relationship A^{2} +
B^{2} = C^{2} is always true.

References
 McAdams, David E.. All Math Words Dictionary, distance. 2nd Classroom edition 201501084799968. pg 6364. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Barnett Rich, Christopher Thomas. Schaum's Outline of Geometry. 4th edition. pg 206. McGrawHill. August 13, 2008. Last Accessed 7/3/2018. Buy the book
 John Sparks. The Student's Essential Formula Book. pg 33. AuthorHouse. July 12, 2004. Last Accessed 7/3/2018. Buy the book
Cite this article as:
McAdams, David E. Distance Formula. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/distanceformula.html.
Image Credits
Revision History
4/20/2019: Updated equations and expressions to the new format (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
1/23/2010: Added "References". (
McAdams, David E.)
12/12/2008: Added manipulative 1. (
McAdams, David E.)
11/25/2008: Changed equations to images. (
McAdams, David E.)
7/12/2008: Changed equations to Hot_Eqn. (
McAdams, David E.)
2/4/2008: Fixed spelling error. (
McAdams, David E.)
7/12/2007: Initial version. (
McAdams, David E.)