What is the distance between #(5,-2,4)# and #(8,8,-1)#?

1 Answer
Shantelle
Apr 29, 2018

#d = sqrt(134)# or #~~ 11.58#

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((-1-4)^2 + (8-(-2))^2 + (8-5)^2)#

Now we simplify:
#d = sqrt((-5)^2 + (10)^2 + (3)^2)#

#d = sqrt(25 + 100 + 9)#

#d = sqrt(134)#

If you want to leave it in exact form, you can leave the distance as #sqrt134#. However, if you want the decimal answer, here it is rounded to the nearest hundredth's place:
#d ~~ 11.58#

Hope this helps!

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