Loading...
Calculate the distance between two points using the distance formula √((x₂−x₁)² + (y₂−y₁)²). Shows step-by-step working with coordinate geometry.
The distance formula calculates the straight-line (Euclidean) distance between two points in a coordinate plane using d = √((x₂−x₁)² + (y₂−y₁)²), derived from the Pythagorean theorem.
Distance
5
Steps
Δx = 4 − 1 = 3
Δy = 6 − 2 = 4
d = √(3² + 4²) = √(9 + 16) = √25
d = 5
Formula
d = √((x₂ − x₁)² + (y₂ − y₁)²)d = Distance between the two points
(x₁, y₁) = Coordinates of the first point
(x₂, y₂) = Coordinates of the second point
Worked Example
Distance from (1, 2) to (4, 6)
Did you know? The distance formula is a special case of the Euclidean metric named after the Greek mathematician Euclid (~300 BC), whose work 'Elements' remained the standard geometry textbook for over 2,000 years (source: Mathematical Association of America).
Sources
Convert between degrees, radians, gradians, turns, and arc units for math and science.
Balance chemical equations by finding the correct coefficients for reactants and products.
Calculate radius, diameter, circumference, area, arc length, and sector area from any input.
Convert between kg/m³, g/cm³, lb/ft³, and more. Includes material density reference.
Differentiate polynomial functions with step-by-step power rule application.
Solve C₁V₁ = C₂V₂ for any missing variable in solution dilution problems.