Is the point A(x, y) in 2rd Quadrant?
1. (x+1 y+1) in 2nd quadrant
2. (x-1, y-1) in 2nd quadrant
If A and B are in the same quadrant, then a*A + (1-a)*B are in that quadrant(if and only if 1 > a > 0). Let a be 1/2 => 1/2(x+1,y+1)+1/2(x-1,y-1) = (x,y). => 1 and 2 together are sufficient.
1 alone is not (-1/2,1/2) is the example.
2 alone is also not sufficient, (-1/2,1/2) is the example again.