ankur.agrawal wrote:In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) Square Root (a^2) + Square root (b^2) = Square root(c^2) + Square root (d^2)

Is there a way to do this without picking values. I mean to say algebraically.

1) is not sufficient to answer the question..!!!
2) can be rephrased as a+b=c+d; which is also not sufficient.

combining 1&2
let a/b=c/d=k;
a=bk,c=dk;
substituting value of a and b in 2 we have;
bk+b=d+dk;
b=d;
if b=d; therefore a=c;
hence distance from origin i.e. Sqrt(a^2+b^2)=sqrt(c^2+d^2) is equal..!!! therefore C