What is the distance between #(-2,1,-3)# and #(5,6,-2)#?

1 Answer
Jan 9, 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)#

Substituting the values from the points in the problem gives:

#d = sqrt((color(red)(5) - color(blue)(-2))^2 + (color(red)(6) - color(blue)(1))^2 + (color(red)(-2) - color(blue)(-3))^2)#

#d = sqrt((color(red)(5) + color(blue)(2))^2 + (color(red)(6) - color(blue)(1))^2 + (color(red)(-2) + color(blue)(3))^2)#

#d = sqrt(7^2 + 5^2 + 1^2)#

#d = sqrt(49 + 25 + 1)#

#d = sqrt(75)#

#d = sqrt(25 * 3)#

#d = sqrt(25)sqrt(3)#

#d = 5sqrt(3)#

Or

#d = 8.660# rounded to the nearest thousandth.