What is the distance between #(7,35,6)# and #(-3,5,1)#?

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Answer 1 · 2016-05-25T11:26:55

#d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2+(z_2-z_1)^2) ~= 32.02#

The distance between two points is simply the square root of the sum of the squares of the differences between the coordinates, or, in equation form:

#d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2+(z_2-z_1)^2)#

where our two points are:

#(x_1, y_1, z_1)# and #(x_2, y_2, z_2)#

It doesn't matter which point you choose for either. Substituting the points we were given into this equation we get:

#d = sqrt((7-(-3))^2 + (35-5)^2+(6-1)^2)#

#d= sqrt(10^2 + 30^2+5^2)#

#d=sqrt(100 + 900+25)#

#d=sqrt(1025) ~= 32.02#