What is the distance between #(-8,9,-1)# and #(4,1,2)#?

1 Answer
SagarStudy
Jan 3, 2016

#sqrt(217)#

Explanation:

The distance formula for Cartesian coordinates is

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2#
Where #x_1, y_1,z_1#, and#x_2, y_2,z_2# are the Cartesian coordinates of two points respectively.
Let #(x_1,y_1,z_1)# represent #(-8,9,-1)# and #(x_2,y_2,z_2)# represent #(4,1,2)#.
#implies d=sqrt((4-(-8))^2+(1-9)^2+(2-(-1))^2#
#implies d=sqrt((12)^2+(-8)^2+(3)^2#
#implies d=sqrt(144+64+9)#
#implies d=sqrt217#

Hence the distance between the given points is #sqrt(217)#.

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