# How do you find the distance between (6,-12) and (12,8)?

May 8, 2017

$\sqrt{436} \approx 20.88 \text{ to 2 dec. places}$

#### Explanation:

$\text{to calculate the distance use the "color(blue)"distance formula}$

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

$\text{the 2 points here are " (6,-12)" and } \left(12 , 8\right)$

$\text{let " (x_1,y_1)=(6,-12)" and } \left({x}_{2} , {y}_{2}\right) = \left(12 , 8\right)$

$d = \sqrt{{\left(12 - 6\right)}^{2} + {\left(8 - \left(- 12\right)\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{{6}^{2} + {20}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{436} \approx 20.88 \text{ to 2 decimal places}$

May 8, 2017

$2 \sqrt{109} \cong 20.88$

#### Explanation:

Use the formula $\sqrt{{\left({y}_{2} - {y}_{1}\right)}^{2} + {\left({x}_{2} - {x}_{1}\right)}^{2}}$

${y}_{1} = 8$
${y}_{2} = - 12$
${x}_{1} = 12$
${x}_{2} = 6$

$= \sqrt{{\left(8 - - 12\right)}^{2} + {\left(12 - 6\right)}^{2}}$

$= 2 \sqrt{109} \cong 20.88$