In the coordinate system are the points (r,s) and (u,v) equidistant from the origin?
Statement 1) r+s=1
Statement 2) u=1-r and v=1-s
Statement 1) r+s=1
Statement 2) u=1-r and v=1-s
The answer is C.
The stem is asking whether sqrt(r^2+s^2)=sqrt(u^2+v^2)
1) We get some information on r and s but we don't know about u and v. So insufficient.
2) We can plug this information into the stem and get:
sqrt(r^2+s^2)=sqrt((1-r)^2+(1-s)^2)=sqrt(1-2r+r^2+1-2s+s^2)=sqrt(2-2(r+s)+r^2+s^2). This alone is also insufficient.
However, if we plug the information that r+s=1 into sqrt(2-2(r+s)+r^2+s^2), we get sqrt(r^2+s^2). Therefore C.
