# What is the distance between (13,23,-1) and (-3,17,2)?

Jan 12, 2016

 d = sqrt301 ≈ 17.35

#### Explanation:

To calculate the distance between the 2 points use the three dimensional form of the distance formula :

 d = sqrt((x_2 - x_1 )^2 + (y_2 - y_1 )^2 + (z_2 - z_1 )^2

$w h e r e \left({x}_{1} , {y}_{1} , {z}_{1}\right) , \left({x}_{2} , {y}_{2} , {z}_{2}\right)$ are 2 points.

In this question let  (x_1 , y_! , z_1 ) = (13 , 23 , - 1 )  and

$\left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(- 3 , 17 , 2\right)$

substitute into the formula :

$d = \sqrt{{\left(- 3 - 13\right)}^{2} + {\left(17 - 23\right)}^{2} + {\left(2 - \left(- 1\right)\right)}^{2}}$

 = sqrt((- 16 )^2 + (-6)^2 + 3^2

$\Rightarrow d = \sqrt{256 + 36 + 9} = \sqrt{301}$ ≈ 17.35 # (2 decimal places