Distance Formula

Introduction:

Distance is a numerical description of how far apart objects are. In physics or everyday discussion, distance may refer to a physical length, or an 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.

The Distance Formula is a variant of the Pythagorean Theorem that you used back in geometry.

The distance between (x₁) and (x₂) is the length of the line segment between them:

D=√(x₂-x₁) ²

The distance is always non-negative, we take only the positive square root. So, the distance between the points P(x1, y1) and Q(x2, y2) is

D=√ [(x₂-x₁)²+(y₂-y₁)²] which is called the distance formula.

In particular, the distance of a point P(x, y) from the origin O(0, 0) is given by

D=√ [x²+y²]