# What is the distance between (7, 4) and (5, 2) ?

Jun 13, 2017

$2 \sqrt{2} \approx 2.828 \text{ to 3 dec. places}$

#### Explanation:

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

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

$\text{the points are } \left({x}_{1} , {y}_{1}\right) = \left(7 , 4\right) , \left({x}_{2} , {y}_{2}\right) = \left(5 , 2\right)$

$\text{substituting into the formula gives}$

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

$\textcolor{w h i t e}{d} = \sqrt{4 + 4}$

$\textcolor{w h i t e}{d} = \sqrt{8}$

$\textcolor{w h i t e}{d} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2}$

$\textcolor{w h i t e}{d} = 2 \sqrt{2} \approx 2.828 \text{ to 3 decimal places}$