# What is the distance between  (4, -5) and  (-6,7) ?

Jan 1, 2016

$2 \sqrt{61}$

#### Explanation:

Use the distance formula which is

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

Now,

$\left({x}_{1} , {y}_{1}\right) = \left(4 , - 5\right) \text{ }$ and $\text{ } \left({x}_{2} , {y}_{2}\right) = \left(- 6 , 7\right)$

Substituting into formula gives

$d = \sqrt{{\left(- 6 - 4\right)}^{2} + {\left[7 - \left(- 5\right)\right]}^{2}}$

$= \sqrt{{\left(- 10\right)}^{2} + {\left(12\right)}^{2}}$

$= \sqrt{100 + 144}$

$= \sqrt{244} = 2 \sqrt{61}$