Question

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

Answer 1

`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`

`where (x_1 , y_1 , z_1 ) , (x_2 , y_2 , z_2 )` are 2 points.

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

`(x_2 , y_2 , z_2 ) = (- 3 ,17 , 2 )`

substitute into the formula :

`d = sqrt ( (- 3 - 13 )^2 + (17 - 23 )^2 + (2 - (-1))^2)`

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

`rArr d = sqrt(256 + 36 + 9 ) = sqrt301` ≈ 17.35 # (2 decimal places