Distance between two points

The distance between two points $A$ and $B$ on the plane is the module of the fixed vector that determines: $d (A, B) = | \vec{A B} |$ In coordinates, if $A = (a_{1}, a_{2})$ and $B = (b_{1}, b_{2})$ , then we have: $d (A, B) = | \vec{A B} | = | (b_{1} - a_{1}, b_{2} - a_{2}) | = \sqrt{(b_{1} - a_{1})^{2} + (b_{2} - a_{2})^{2}}$

Example

To calculate the distance between points $A = (3, 4)$ and $B = (2, - 5)$ . $d (A, B) = | \vec{A B} | = | (2 - 3, - 5 - 4) | = | (- 1, - 9) | = \sqrt{(- 1)^{2} + (- 9)^{2}} = \sqrt{82}$