Mathguru – Help – How to find a point on the X-axis equidistant from two given points?

Solved Example > No. SE 1

How to find a point on the X-axis equidistant from two given points?

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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:

$d=\sqrt{(\Delta x)^2}=\sqrt{(x_2-x_1)^2}.\,$

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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.\,$ (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:

$d=\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}.$

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.