What is the distance between #(3, –1, 1) # and #(4, 1, –3) #?

1 Answer
Alan P.
Jan 4, 2016

#sqrt(21)#

Explanation:

The 3-D version of the Pythagorean Theorem tells us that that distance between two points #(x_1,y_1,z_1)# and #(x_2,y_2,z_2)# is
#color(white)("XXXXX")sqrt((Deltax)^2+(Delta y)^2+(Delta z)^2)#

#color(white)("XXX")=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

In this case with points #(3,-1,1)# and #(4,1,-3)#
the distance is
#color(white)("XXX")sqrt((4-3)^2+(1-(-1))^2+((-3)-1)^2)#

#color(white)("XXX")=sqrt(1^2+2^2+(-4)^2)#

#color(white)("XXX")=sqrt(21)#

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