What is the distance between #(8,1,-4)# and #(-3,6,-2)#?

1 Answer
Apr 29, 2018

Answer:

#d = 5sqrt6# or #~~ 12.25#

Explanation:

The formula for the distance for 3-dimensional coordinates is similar or 2-dimensional; it is: #d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)#

We have the two coordinates, so we can plug in the values for #x#, #y#, and #z#:
#d = sqrt((-2-(-4))^2 + (6-1)^2 + (-3-8)^2)#

Now we simplify:
#d = sqrt((2)^2 + (5)^2 + (-11)^2)#

#d = sqrt(4 + 25 + 121)#

#d = sqrt(150)#

#d = 5sqrt6#

If you want to leave it in exact form, you can leave the distance as #5sqrt6#. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
#d ~~ 12.25#

Hope this helps!