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

1 Answer
Jan 12, 2016

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 #(-5,-1,1)# and #(x_2,y_2,z_2)# represent #(4,-1,2)#.
#implies d=sqrt((4-(-5))^2+(-1-(-1))^2+(2-1)^2#
#implies d=sqrt((4+5)^2+(-1+1)^2+(2-1)^2#
#implies d=sqrt((9)^2+(0)^2+(1)^2#
#implies d=sqrt(81+0+1#
#implies d=sqrt(82#
#implies d=sqrt(82# units

Hence the distance between the given points is #sqrt(82)# units.