# What is the distance between (3, –1, 1)  and (0, 4, –2) ?

Mar 31, 2018

$\sqrt{43} \approx 6.557 \text{ to 3 dec. places}$

#### Explanation:

$\text{using the 3 dimensional form of the "color(blue)"distance formula}$

•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)

$\text{let } \left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(3 , - 1 , 1\right)$

$\text{and } \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(0 , 4 , - 2\right)$

$d = \sqrt{{\left(0 - 3\right)}^{2} + {\left(4 + 1\right)}^{2} + {\left(- 2 - 1\right)}^{2}}$

$\textcolor{w h i t e}{d} = \sqrt{9 + 25 + 9} = \sqrt{43} \approx 6.557$