Please refer to the attachment.

The answer to the question is C.

Can someone explain why the answer is not B, as well as the underlying geometry principles this question is testing.

Can someone please highlight an actual numerical example when (r, s) and (1-r, 1-s) are both equidistant from the origin?

Thank you!

Distance from origin is x^2+y^2

r,s distance is r^2+s^2

(1-r), (1-s) distance is (1-r)^2+(1-s)^2 = 1+r^2-2r+1+s^2-2s = r^2+s^2 + 2(1-r-s) which is same as r,s distance if r+s = 1, since in that case, 1-r-s = 0.

Numerical example,

2,2 is not at the same ditance from origin as 1,1 (which is 2-1, 2-1).
But if we take a example where r+s = 1

say 1/2, 3/2 then 1-1/2, 1-3/2 (effectively 3/2, 1/2) is same distance as 1/2,3/2.

Your post was helpful.

thank you.