What is the distance between M(7,−1,5) and the origin?

1 Answer
Aug 14, 2014

The answer is 5sqrt(3).

We simply use the Pythagorean Theorem for this calculation. We can draw a right triangle on the xy plane and extend this for another right triangle to the z plane. Let d be the length of the diagonal on the xy plane. Then

l=sqrt(d^2+z^2)

but

d^2=x^2+y^2

so

l=sqrt(x^2+y^2+z^2)

and substituting the values from your question:

l=sqrt(7^2+(-1)^2+5^2)=sqrt(49+1+25)=sqrt(75)=5sqrt(3)

We can generalize the distance between any 2 - 3D points as:

l=sqrt((P_(2_x)-P_(1_x))^2+(P_(2_y)-P_(1_y))^2+(P_(2_z)-P_(1_z))^2)

The order of P_1 and P_2 doesn't matter because the difference is squared which always results in a positive value.