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

1 Answer
David B.
May 25, 2016

d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2+(z_2-z_1)^2) ~= 32.02d=√(x2−x1)2+(y2−y1)2+(z2−z1)2≅32.02

Explanation:

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)d=√(x2−x1)2+(y2−y1)2+(z2−z1)2

where our two points are:

(x_1, y_1, z_1)(x1,y1,z1) and (x_2, y_2, z_2)(x2,y2,z2)

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=√(7−(−3))2+(35−5)2+(6−1)2

d= sqrt(10^2 + 30^2+5^2)d=√102+302+52

d=sqrt(100 + 900+25)d=√100+900+25

d=sqrt(1025) ~= 32.02d=√1025≅32.02

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