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smallsorrow wrote:in the xy-plane, are points (r,s) and (u,v) equidistant from the origin

1) r+s =1
2) u=1-r ; v=1-s

IMO its E but it is C. can anyone pls explain?

Thanks!

from 1.) r+s = 1 , it does nt give any info regarding u or v... so insuff...
eliminate a,d
from 2.) also we can get any value for u and v. so eliminate b
now combining 1.) and 2.)
from 1.) we can get r = 1-s or s = 1-r
so, in 2.) it is given that u=s and v=r
and we know the distance of (a,b) from origin is sqrt(a^2+b^2).
so, either we write sqrt(r^2+s^2) or sqrt(s^2+r^2) its same.
so ans is C.
hope it helps..

in the xy-plane, are points (r,s) and (u,v) equidistant from the origin

1) r+s =1
2) u=1-r ; v=1-s


To make points equidistant they should fit circumference formula
radius^2 = x^2 + y^2
so to make points (r,s) and (u,v) equidistant they should fit
r^2 + s^2 = y^u + v^2


(1)
Clearly INSUFF

(2)
Substitute u=1-r and v=1-s to r^2 + s^2 = y^u + v^2
Finally you'll get r+s=1
Only in this case (r,s) and (u,v) will be equidistant
But (2) alone do not state this


(1)(2)
(1) gives necessary equation for (2)
SUFF


C