**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

=> 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)**