Concept:  The question tests on applications of coordinate geometry
Solution:
(-a, b) and (-b, a) are in the same quadrant
 => x-coordinates & have the same sign
=> They either could both be positive (Quadrant I) or
      They could both be negative (in which case, the points would be in Quadrant IV)
St(1):- xy > 0
=> x and y have the same sign
=>both positive or both negative.
 a & b have the same sign, and x & y have the same sign,
but there's two possibilities for each(++/--), so we don't know whether (a & b) & (x & y) all have the same sign. (Insufficient)
St(2):- a x > 0
a and x have the same sign
=>with this alone, we know that a & b & x all have the same sign, but no information about y. (Insufficient)
Combining both,
x & y & a & b all have the same sign.
=> (-x, y) will have the same sign of x- & y-coordinates as (-a, b) & (-b, a),
=>all will be in the same quadrant. (sufficient)  (option c)