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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