(1) is clearly not sufficient.
(2) is also not sufficient - substitute (r, s) as (0,0), then (u,v) is (1,1) - i.e. distances are not the same. But substitute (r,s) as (1,0), then (u,v) is (0, 1) - i.e. the distances are the same.
Now, together, I think they are sufficient to solve. What follows is mostly algebra.
The distance for (r,s) from origin is sqrt(r^2 + s^2)
The distance for (u,v) from origin in terms of r,s is:
sqrt[(1-r)^2 + (1-s)^2].
Simplify => sqrt(r^2 + s^2 - 2r - 2s +2).
Substitue r+s = 1 => sqrt(r^2 + s^2).
Which is the same as the distance for (r,s).
Hence (C)
