Explanation:
Distance is a numerical
description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical
length, or estimation based on other criteria (e.g. "two counties
over"). In mathematics, a distance function or metric is a generalization of the concept of physical distance. A
metric is a function that behaves according to a specific set of rules, and
provides a concrete way of describing what it means for elements of some space
to be "close to" or "far away from" each other.
In most cases, "distance from A to B" is interchangeable
with "distance between B and A".
Geometry
In neutral geometry,
the distance between (x_{1}) and (x_{2}) is the
length of the line segment between them:
In analytic
geometry, the distance between two points of the xy-plane can be found using the distance
formula. The distance between (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by:
(Our solved example in mathguru.com uses this concept)
Similarly, given points (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) in three-space, the distance between them
is:
These formulae are easily derived by constructing a right triangle
with a leg on the hypotenuse of another (with the other leg orthogonal to the plane that contains the 1st triangle) and
applying the Pythagorean Theorem.
http://en.wikipedia.org/wiki/Distance
The above explanation is copied from Wikipedia, the free
encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.