# Distance Formula

How to find the distance between two points: formula, proof, example, and its solution.

## Formula

The distance between two points (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}) is

√(*x*_{2} - *x*_{1})^{2} + (*y*_{2} - *y*_{1})^{2}.

## Proof

(purple) = *x*_{2} - *x*_{1}, (blue) = *y*_{2} - *y*_{1}

Then, by the Pythagorean theorem,*d*^{2} = (*x*_{2} - *x*_{1})^{2} + (*y*_{2} - *y*_{1})^{2}.

So *d* = √(*x*_{2} - *x*_{1})^{2} + (*y*_{2} - *y*_{1})^{2}.

## Example

Put (-3, 1) and (5, 4) into the formula.