Distance & Midpoint Formulas
Distance & Midpoint
- Distance
- d = √((x2 − x1)2 + (y2 − y1)2)
- Midpoint
- M = ((x1 + x2) ⁄ 2, (y1 + y2) ⁄ 2)
- Slope
- m = (y2 − y1) ⁄ (x2 − x1)
- (x₁, y₁) first point
- (x₂, y₂) second point
Distance & Midpoint formulas explained
The distance between two points on a coordinate plane is the Pythagorean theorem applied to the horizontal and vertical gaps. Below are all the distance formula with what each letter means, a worked example and a free calculator.
- Distance:
d = √((x₂ − x₁)² + (y₂ − y₁)²) - Midpoint:
M = ((x₁ + x₂) ⁄ 2, (y₁ + y₂) ⁄ 2) - Slope:
m = (y₂ − y₁) ⁄ (x₂ − x₁)
Distance & Midpoint calculator
Distance & Midpoint calculator
Worked example: distance of a distance & midpoint
Given x₁ = 1 cm, y₁ = 2 cm, x₂ = 7 cm, y₂ = 10 cm, substitute the values into each distance & midpoint formula:
- d = √((7 − 1)² + (10 − 2)²) = 10 cm
- Mₓ = (1 + 7) ⁄ 2 = 4
- Mᵧ = (2 + 10) ⁄ 2 = 6
- m = (10 − 2) ⁄ (7 − 1) = 1.33
Distance & Midpoint formulas FAQ
What is the distance formula?
The distance formula is d = √((x₂ − x₁)² + (y₂ − y₁)²), where (x₁, y₁) is the first point, (x₂, y₂) is the second point.
What is the midpoint formula?
The midpoint formula is M = ((x₁ + x₂) ⁄ 2, (y₁ + y₂) ⁄ 2), where (x₁, y₁) is the first point, (x₂, y₂) is the second point.
What is the slope formula?
The slope formula is m = (y₂ − y₁) ⁄ (x₂ − x₁), where (x₁, y₁) is the first point, (x₂, y₂) is the second point.
Can I download the distance & midpoint formulas as a PDF?
Yes. Use the Download PDF button on this page for a free printable distance & midpoint formula sheet with a worked example and practice questions.