# What is the distance between (–10, –2, 2)  and (–2, 2, 6) ?

Apr 21, 2018

color(indigo)("Distance between the two points" = 9.8 " units"

#### Explanation:

$\left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(- 10 , - 2 , 2\right) , \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(- 2 , 2 , 6\right)$

color(crimson)(d = sqrt((x_2 - 1)^2 + (y_2 - y_1)^2 + (z_2-z_1)^2)

$d = \sqrt{{\left(- 2 + 10\right)}^{2} + {\left(2 + 2\right)}^{2} + {\left(6 - 2\right)}^{2}}$

$d = \sqrt{{8}^{2} + {4}^{2} + {4}^{2}} = \sqrt{96}$

color(indigo)("Distance between the two points " d = 9.8 " units"