Euclidean distance

In Euclidean geometry, the Euclidean distance is the usual distance between two points "p" and "q". This distance is measured as a line segment. The Pythagorean theorem can be used to calculate this distance. 
Euclidean distance on the plane.
In the Euclidean plane, if p = ("p"1, "p"2) and q = ("q"1, "q"2) then the distance is given by
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 ("r"1, θ1) and those of q are ("r"2, θ2), then the distance between the points is