What is the distance between #(13,-23,-20)# and #(-3,-37,-22)#?

1 Answer
Jun 23, 2018

Answer:

See a solution process below:

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)#

Where #(color(blue)(x_1), color(blue)(y_1), color(blue)(z_1))# and #(color(red)(x_1), color(red)(y_1), color(red)(z_1))# are two points.

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(-37) - color(blue)(-23))^2 + (color(red)(-22) - color(blue)(-20))^2)#

#d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(-37) + color(blue)(23))^2 + (color(red)(-22) + color(blue)(20))^2)#

#d = sqrt((-16)^2 + (-14)^2 + (-2)^2)#

#d = sqrt(256 + 196 + 4)#

#d = sqrt(456)#

#d = sqrt(4 * 114)#

#d = sqrt(4)sqrt(114)#

#d = 2sqrt(114)#

Or, approximately:

#d ~= 21.354#