In the rectangular coordinate system, are the points (r,s) and (u,v) equidistant from the origin?
condition 1: r +s = 1
condition 2: u = 1 -r and v = 1 - s
FYI: I got the answer by picking numbers. Can someone please explain the "correct" mathematically method for solving this problem? Specifically, how does the constraint given by condition 1 algebrically relate to condition 2? Thanks for your help.
For points to be equidistant from origin (0,0)
Sqrt(r^2 + s^2) = Sqrt(u^2 + v^2)
r^2 + s^2 =u^2 + v^2
s^2-v^2 = u^2-r^2
(s-v)(s+v) = (u-r)(u+r) --- A
Statement 1 - Insufficient as says nothing about u & v
Helps us reduce condition A to
(s-v) = (u-r)
s+r = u+v
= 2 -(r+s)
r+s = 1 --- this condition is still not satisfied by Statement 2 - Hence Insuff
Together sufficient as we get r+s = 1 from Statement 1