What is the distance between #(–6, 3, 1) # and #(5, 6, 4) #?

1 Answer
Apr 29, 2018

Answer:

#d ~~ 11.79#

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((5-(-6))^2 + (6-3)^2 + (4-1)^2)#

Now we simplify:
#d = sqrt((11)^2 + (3)^2 + (3)^2)#

#d = sqrt(121 + 9 + 9)#

#d = sqrt(139)#

If you want to leave it in exact form, you can leave the distance as #sqrt139#. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
#d ~~ 11.79#

Hope this helps!