a*b is not equal to 0. (-a,b) and (-b,a) are in the same quadrant of the (x,y) plane. is ( -x,y) in the same quadrant.
1) xy>0
2) ax>0
OA C
I would've picked E.
1) xy>0
2) ax>0
OA C
I would've picked E.
From the given information, (-a,b) and (-b,a) are in the same quadrant, it means two things:
first, -a & -b are both positive or negative (1)
second, b & a are both positive or negative (2)
(1)&(2) suggest that a*b > 0
So if a>0 then (-a,b) will be in Quadrant 1
if a<0 then (-a,b) will be in Quadrant 3.
First premise: x*y> 0 so (-x,y), like (-a,b) can both be in quadrant 1 or 3, however, we do not know whether a & x have the same sign ( + or -). So (-a,b) can be in Q1 if a>0, and (-x,y) can be in Q3 if x<0. => Insuff
Second premise alone : ax>0, we can not determine the sign of y and x, so can not determine the Quadrant the point is in either.
But, combine with the 1st premise, we'll see that a & x have the same sign, so (-a,b) and (-x,y) have the same properties - both stay in Q1 if a>0 and x>0 and in Q3 if a<0 and x<0.
So C. Sorry for my poor drawing.
