What is the distance between #(43,2,11)# and #(7,-1,26)#?

1 Answer
May 28, 2018

Answer:

The distance is #3sqrt170# or #~~ 39.12#.

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((26-11)^2 + (-1-2)^2 + (7-43)^2)#

Now we simplify:
#d = sqrt((15)^2 + (-3)^2 + (-36)^2)#

#d = sqrt(225 + 9 + 1296)#

#d = sqrt(1530)#

#d = sqrt(9*170)#

#d = sqrt9sqrt170#

#d = 3sqrt170#

If you want to leave it in exact form, you can leave the distance as #3sqrt170#. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
#d ~~ 39.12#

Hope this helps!