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Distance Formula

Distance Formula

One-page printable reference

See It in Action

Two examples of the idea done right—and one common look-alike that is not right.

EXAMPLE

EXAMPLE

NON-EXAMPLE

Definition

The distance formula is a mathematical equation used to calculate the distance between two points in the coordinate plane.

Definition:

The distance formula is a formula used to find the straight-line distance between two points (x1, y1) and (x2, y2) on the coordinate plane.

The Formula:

The square root of open parentheses x two minus x one close parentheses squared plus open parentheses y two minus y one close parentheses squared.

Origin:

  • This formula comes from the Pythagorean Theorem, where the horizontal and vertical differences between points form the legs of a right triangle.

Example:

To find the distance between points (1, 2) and (4, 6):


The square root of open parentheses four minus one close parentheses squared plus open parentheses six minus two close parentheses squared equals the square root of three squared plus four squared equals the square root of nine plus sixteen equals the square root of twenty five equals five.

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