# What is the distance between (0,0) and (-15,36)?

May 13, 2016

$39$

#### Explanation:

From Pythagoras theorem, we get the following formula for the distance between points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ in the plane:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

In our example, $\left({x}_{1} , {y}_{1}\right) = \left(0 , 0\right)$ and $\left({x}_{2} , {y}_{2}\right) = \left(- 15 , 36\right)$, giving us:

$d = \sqrt{{\left(- 15 - 0\right)}^{2} + {\left(36 - 0\right)}^{2}}$

$= \sqrt{{\left(- 15\right)}^{2} + {36}^{2}}$

$= \sqrt{225 + 1296}$

$= \sqrt{1521} = 39$