With the distance formula, I have seen that instead of people using d = square root of [ (X2 - X1)^2 + (Y2 - Y1)^2], they do this:

d^2 = (X2 - X1)^2 + (Y2 - Y1)^2
^ So they square both sides, and then they say that let S = d^2, meaning let this be the distance. Why is this the same as the first?

Question

With the distance formula, I have seen that instead of people using d = square root of [ (X2 - X1)^2 + (Y2 - Y1)^2], they do this:

d^2 = (X2 - X1)^2 + (Y2 - Y1)^2 
^ So they square both sides, and then they say that let S = d^2, meaning let this be the distance. Why is this the same as the first?

anonymous · Answer

it is not the distance, it is the square of the distance, but it is usually easier to work with with because there are no annoying square roots

anonymous · Answer

a calculus problem for example that would ask "what is the point  closest to...?" it would be easier to work with the square of the distance than the distance

anonymous · Answer

d = square root of [ (X2 - X1)^2 + (Y2 - Y1)^2], they do this:
d^2 = (X2 - X1)^2 + (Y2 - Y1)^2  squaring both side 
then u got confused because S=d^2 right? 
then u can write S=(X2 - X1)^2 + (Y2 - Y1)^2 it is just they supposed 
s as d^2