What is the distance between #(-5,13,4)# and #(2,-16,-2)#?

1 Answer
radee
Feb 5, 2016

#d ~~ 30.4302#

Explanation:

We know that the distance formula for cartesian coordinates is as follows:

#sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)#

In the case where there are three dimensions #(x, y, z)#, you just need to add another term to account for the z-coordinates.

#sqrt((x_2-x_1)^2 + (y_2 - y_1)^2 + (z_2 -z_1)^2)#

Plugging in the values from the given...

[Given]
#P_1: (-5, 13, 4)#
#P_2: (2, -16, -2)#

[Solution]
#d = sqrt((2-(-5))^2 + (-16-13)^2 + (-2-4)^2)#
#d = sqrt(7^2 + (-29)^2 + (-6)^2)#
#d = sqrt(49 + 841 + 36)#
#d = sqrt (926)#
#d ~~ 30.4302#

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