Coordinate Geometry

Distance Between Two Points

Formula

d = √((x₂ − x₁)² + (y₂ − y₁)²)

What is Distance Between Two Points?

The distance between two points in a coordinate plane is found using the distance formula, which is derived from the Pythagorean theorem.

Variables

d
d — Distance between the two points
(
(x₁, y₁) — Coordinates of the first point
(
(x₂, y₂) — Coordinates of the second point

Worked Examples

Example 1

Find the distance between (1, 2) and (4, 6).

Solution:

d = √((4−1)² + (6−2)²) = √(9 + 16) = √25 = 5

Frequently Asked Questions

Related Formulas

Slope of a Line

m = (y₂ − y₁) / (x₂ − x₁)

Midpoint Formula

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Equation of a Line (Slope-Intercept Form)

y = mx + c

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