if ab does not = 0, and points (-a,b)(-b,a) are in the same quadrant of the xy plane, is point (-x,y) in the same quadrant?
(1) xy>0
(2) ax>0
(1) xy>0
(2) ax>0
Think the answer is C
My approach was as under:
The problem states that (-a,b)(-b,a) are in the same xy plane. This can be true only when in cases where
- Both a and b have a positive value or
- Both a and b have a negative value
(given that ab is not equal to zero)
With this information we can use (2) which says ax>0. This means that x retains the sign of a. If a is a positive value, then x is positive and if a is negative, x is negative to make ax>0.
Now (1) tells us that xy>0 and hence y retains the sign of x.
Hence for any set of values for a and b (fulfilling the above 2 conditions)
(-x,y) would be in the same quadrant as (-a,b)(-b,a).
