How do you find the distance between the points (9,-12), (3,-6)?

Feb 6, 2017

$6 \sqrt{2}$

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 (9 ,-12) and (3 ,-6)

let $\left({x}_{1} , {y}_{1}\right) = \left(9 , - 12\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(3 , - 6\right)$

$d = \sqrt{{\left(3 - 9\right)}^{2} + {\left(- 6 + 12\right)}^{2}} = \sqrt{36 + 36} = \sqrt{72}$

$\sqrt{72} \text{ may be simplified}$

$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6 \sqrt{2} \leftarrow \text{ exact value}$