# How do you use the distance formula to find the distance of W(1,7), X(-2,-4)?

Jan 12, 2017

sqrt130≈11.40

#### Explanation:

Using the $\textcolor{b l u e}{\text{distance formula}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) , \left({x}_{2} , {y}_{2}\right) \text{ are 2 coordinate points}$

The 2 points here are (1 ,7) and (-2 ,-4)

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

substituting into the distance formula.

$d = \sqrt{{\left(- 2 - 1\right)}^{2} + {\left(- 4 - 7\right)}^{2}} = \sqrt{{\left(- 3\right)}^{2} + {\left(- 11\right)}^{2}}$

$= \sqrt{9 + 121} = \sqrt{130} \leftarrow \text{ exact value}$

sqrt130≈11.40" to 2 decimal places"