What is the distance between #(-7,6,10)# and #(7,-4,9)#?

1 Answer
Steve M
Mar 29, 2018

distance #=3sqrt(33) ~~ 17.2 # square units

Explanation:

We seek the distance #d#, say, between the coordinates #(-7,6,10)# and #(7,-4,9)#? in euclidean space.

Applying Pythagoras theorem in #3#-Dimensions we have:

# d^2 = (-7-7)^2 + (6-(-4))^2 + (10-9)^2 #
# \ \ \ \ = (-14)^2 + (10)^2 + (1)^2 #
# \ \ \ \ = 196 + 100 + 1 #
# \ \ \ \ = 297 #

Thus:

# d = sqrt(297) \ \ \ # (NB - we seek the positive solution)
# \ \ = sqrt(9*33) #
# \ \ = 3sqrt(33) #
# \ \ ~~ 17.2 #

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