From the information provided in the question here're several possibilities:
1. a=2, b=2 => (-a,b) = -2, 2 & (-b,a) = -2, 2 - valid since the points fall in same quadrant - IInd
2. a=-2, b=2 => (-a, b) = 2,2 & (-b,a) = -2, -2 - invalid since the points fall in different quadrant
3. a=2, b=-2 => (-a, b) = -2,-2 & (-b,a) = 2, 2 - invalid since the points fall in different quadrant
4. a=-2, b=-2 => (-a,b) = 2,-2 & (-b,a) = 2, -2 - valid since the points fall in same quadrant - IVth
From the information above you know that (-a,b) and (-b,a) are either in IInd or IVth quadrant
Now consider the data
i) xy > 0 merely says that x and y are both +ve or both -ve. This means that the point (-x, y) falls either in IInd quadrant or IVth quadrant - Insufficient on its own
ii) ax>0 merely tells the same thing. either a and x are both +ve or both -ve. That again means (-x,y) falls either in IInd or IVth quadrant - Insufficient on its own
But combining i) and ii) there are two possibilities
1) (-a, b) and (-b,a) are in IInd quadrant,
a must be +ve and from ii) x is +ve; so from i) y should be +ve too. Thus (-x, y) lies in IInd quadrant
2) (-a, b) and (-b,a) are in IVth quadrant,
a must be -ve and from ii) x is -ve; so from i) y should be -ve too. Thus (-x, y) lies in IVth quadrant.
Was a tough one. I had to scratch my head hard!
1. a=2, b=2 => (-a,b) = -2, 2 & (-b,a) = -2, 2 - valid since the points fall in same quadrant - IInd
2. a=-2, b=2 => (-a, b) = 2,2 & (-b,a) = -2, -2 - invalid since the points fall in different quadrant
3. a=2, b=-2 => (-a, b) = -2,-2 & (-b,a) = 2, 2 - invalid since the points fall in different quadrant
4. a=-2, b=-2 => (-a,b) = 2,-2 & (-b,a) = 2, -2 - valid since the points fall in same quadrant - IVth
From the information above you know that (-a,b) and (-b,a) are either in IInd or IVth quadrant
Now consider the data
i) xy > 0 merely says that x and y are both +ve or both -ve. This means that the point (-x, y) falls either in IInd quadrant or IVth quadrant - Insufficient on its own
ii) ax>0 merely tells the same thing. either a and x are both +ve or both -ve. That again means (-x,y) falls either in IInd or IVth quadrant - Insufficient on its own
But combining i) and ii) there are two possibilities
1) (-a, b) and (-b,a) are in IInd quadrant,
a must be +ve and from ii) x is +ve; so from i) y should be +ve too. Thus (-x, y) lies in IInd quadrant
2) (-a, b) and (-b,a) are in IVth quadrant,
a must be -ve and from ii) x is -ve; so from i) y should be -ve too. Thus (-x, y) lies in IVth quadrant.
Was a tough one. I had to scratch my head hard!
