Euclidean distance

Euclidean distance in R²

In the Euclidean plane, if p = (p₁, p₂) and q = (q₁, q₂) then the distance is given by[3]

${\displaystyle d(\mathbf {p} ,\mathbf {q} )={\sqrt {(q_{1}-p_{1})^{2}+(q_{2}-p_{2})^{2}}}.}$

This is equivalent to the Pythagorean theorem, where legs are differences between respective coordinates of the points, and hypotenuse is the distance.

Alternatively, if the polar coordinates of the point p are (r₁, θ₁) and those of q are (r₂, θ₂), then the distance between the points is

${\displaystyle d(\mathbf {p} ,\mathbf {q} )={\sqrt {r_{1}^{2}+r_{2}^{2}-2r_{1}r_{2}\cos(\theta _{1}-\theta _{2})}}.}$

• Norm (mathematics)
• Polar coordinates

1. Weisstein, Eric W. "Distance". mathworld.wolfram.com. Retrieved 2020-09-01.
2. "Distance Between 2 Points". www.mathsisfun.com. Retrieved 2020-09-01.
3. "Distance Between 2 Points". www.mathsisfun.com. Retrieved 2020-09-01.