$d(x, y) = \sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2}$ on $\reals^2$

Example · High school

The Euclidean distance between points in the plane.

Terms

Term	This example	Why
metric	✓	The Euclidean distance is a metric, and it comes from the Euclidean norm, as $d(x, y) = \norm{x - y}$.

Distinctions using this example

• Norm vs. metric vs. inner product

All examples · All distinctions · All definitions