What is the distance between #(-5,3,9)# and #(-1,-4,1)#?

1 Answer
Shantelle
Jul 25, 2018

The distance is #sqrt129# or about #11.358# (rounded to nearest thousandth's place).

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-(-5))^2 + (-4-3)^2 + (1-9)^2)#

Now we simplify:
#d = sqrt((4)^2 + (-7)^2 + (-8)^2)#

#d = sqrt(16 + 49 + 64)#

#d = sqrt(129)#

If you want to leave it in exact form, you can leave the distance as #sqrt129#. However, if you want the decimal answer, here it is rounded to the nearest thousandth's place:
#d ~~ 11.358#

Hope this helps!

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