# What is the distance between (-2,1) and  (3,7) ?

Dec 7, 2015

The distance between $\left(- 2 , 1\right)$ and $\left(3 , 7\right)$ is $\sqrt{61}$ units.

#### Explanation:

We can use the distance formula to find the distance between any two given points, where $d =$the distance between the points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$:

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

If we plug in our points, our equation will be:

$d = \sqrt{{\left(3 - \left(- 2\right)\right)}^{2} + {\left(7 - 1\right)}^{2}}$

This can be simplified to d = sqrt((5)^2 + (6)^2

And then: d = sqrt((25) + (36), which is $d = \sqrt{61}$.

You can't simplify this further, so your final answer is $\sqrt{61}$ units.

Usually, the square root of a quantity would be $+$ or $-$ , but in this case, the quantity is only positive because it represents distance, which can never be negative.