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Example:Find Point using Distance Formula

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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 (x1) and (x2) 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 (x1, y1) and (x2, y2) is given by:

(Our solved example in mathguru.com uses this concept)

Similarly, given points (x1, y1, z1) and (x2, y2, z2) 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.