If ab ≠ 0, in which quadrant of the coordinate system does point (a, b) lie?

(1) (-b, a) lies in quadrant I.

(2) (-a, b) lies in quadrant III.


Ans: ab ≠ 0 says that neither a or b =0 so the point (a,b) will not lie on the X or Y axis.


Statement 1: (-b, a) lies in quad I so we can infer that -b and a both are positive numbers, because in quadrant I both co-ordinates take a positive value.This implies that a is positive but b is negative (because -b is +ve so b is -ve). Thus point (a,b) will lie in quadrant where X co-ordinate is +ve and Y is -ve i.e. quadrant IV. STATEMENT 1 --> Sufficient

Statement 2: (-a, b) lies in quad III so we can infer that -a and b both are negative numbers, because in quadrant III both co-ordinates take a negative value.This implies that a is positive but b is negative (because (-a) is -ve so a is +ve). Thus point (a,b) will lie in quadrant where X co-ordinate is +ve and Y is -ve i.e. quadrant IV. STATEMENT 2 --> Sufficient

Answer D