GMATPrep - Equidistance coordinate

we have to prove u^2+v^2=r^2+s^2
stmt 1 - not suff
stmt2
u=1-r squaring both sides....u^2=1-2r+r^2 ....eqn1
v=1-s squaring both sides....v^2=1-2s+s^2.....eqn2
adding eqn1 and eqn2
u^2 + v^2=2-2r-2s+r^2 +s^2 ..not suff
combining 1 and 2
u^2 + v^2=2-2r-2s+r^2 +s^2
u^2 + v^2=2-2(r+s)+r^2 +s^2
substituting stm1
u^2 + v^2=2-(2*1)+r^2 +s^2
u^2 + v^2=r^2 +s^2...sufff....hence answer is 'C'..

bha wrote:we have to prove u^2+v^2=r^2+s^2

I guess I was missing this fundamental concept of finding a distance of a point from origin.

Thanks for solution. For others:

Distance of point (r,s) from origin can be found by

d^2 = (s-0)^2 + (r-0)^2 ----- (i)

Distance of point (u,v) from origin:

d^2 = (v-0)^2 + (u-0)^2 ------ (ii)

To prove whether they are equidistant: From (i) and (ii)

(s)^2 + (r)^2 = (v)^2 + (u)^2

and then the rest is solved in the above thread ..