In the rectangular coordinate system, are the points (r,s) and (u,v)

In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?

(1) r + s = 1

(2) u = 1 - r and v = 1 - s

Distance between the point A (x,y) and the origin can be found by the formula: \(D=\sqrt{x^2+y^2}\).

Basically the question asks is \(\sqrt{r^2+s^2}=\sqrt{u^2+v^2}\) OR is \(r^2+s^2=u^2+v^2\)?

(1) \(r+s=1\), no info about \(u\) and \(v\);

(2) \(u=1-r\) and \(v=1-s\) --> substitute \(u\) and \(v\) and express RHS using \(r\) and \(s\) to see what we get: \(RHS=u^2+v^2=(1-r)^2+(1-s)^2=2-2(r+s)+ r^2+s^2\). So we have that \(RHS=u^2+v^2=2-2(r+s)+ r^2+s^2\) and thus the question becomes: is \(r^2+s^2=2-2(r+s)+ r^2+s^2\)? --> is \(r+s=1\)? We don't know that, so this statement is not sufficient.

(1)+(2) From (2) question became: is \(r+s=1\)? And (1) says that this is true. Thus taken together statements are sufficient to answer the question.

Answer: C.

Hope it helps.