What is the distance between #(1,-10,-3)# and #(4,3,-2)#?

1 Answer
Feb 13, 2017

Answer:

The distance between the points is #sqrt(179)# or #13.379# rounded to the nearest thousandth.

Explanation:

The formula for calculating the distance between two points is:

#d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2 + (color(red)(z_2) - color(blue)(z_1))^2)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(4) - color(blue)(1))^2 + (color(red)(3) - color(blue)(-10))^2 + (color(red)(-2) - color(blue)(-3))^2)#

#d = sqrt((color(red)(4) - color(blue)(1))^2 + (color(red)(3) + color(blue)(10))^2 + (color(red)(-2) + color(blue)(3))^2)#

#d = sqrt(3^2 + 13^2 + 1^2)#

#d = sqrt(9 + 169 + 1)#

#d = sqrt(179) = 13.379#