on a xy plane the quadrant in which a point lies on is determined by th sign of that point ..lanter1 wrote:If ab is not equal to zero and points (-a,b) and (-b,a) are int he same quadrant of the xy plane, is point (-x,y) in this same quadrant?
1) xy>0
2) ax>0
the question says that (-a,b) and (-b,a) are in the same quadrant .. that means that a and b have the same sign .. if both are positive then the points lie in the 2nd quadrant ... and if both are negative then the points lie in the 4th quadrant ..
Now, the question asks if (-x,y) lies in the same quadrant as (-a,b) and (-b,a) .. this will be true only if 'x' and 'y' have the same sign as 'a' and 'b' ..
look at the first statement .. it says xy> 0 .. this means that x and y have the same sign but it says nothing about the sign of a and b .. so this statement is insufficient ..
the 2nd statement says ax> 0 that means a,b and x have the same sign .. but y culd still have a different sign .. so this statement is again insufficient ..
Combine both the statements and we get that all the four variables have the same sign .. so sufficient .. so the answer is C ..
