coordinate point

[billyr]

Please help explain the questions above.


thanks

[hk]

Can anybody please explain this???

[x2suresh]

Given ab<>0
(-a,b),(-b,a) are on the same quadrant.

clearly from the above. -a and -b have same sign also a and b have same sign.

ab>0 ( both are -ve or +ve)

these points exists in either I quadrant or III quadrant.

(1) xy>0

clearly not sufficient. We don't how they are related to either x or y

(2) ax>0

ax>0 clearly tells the a and x HAVE same sign.

but we don't know the sign of y.

not sufficient


combined

a,b,y,z have same sign.


(-a,b),(-b,a) (-x,y) exists in same quadrant ( It can be either I or III)

Question: is (-X,Y) same quadrant? "Ans" : Yes.

Sufficient.

C

[Uri]

Testing with different numbers [eg. (2,3), (-2,3), (-2,-3) and (2,3)], we find that he points are in the 2nd quadrant.

(1) implies that x and y are either in the 1st quadrant or in the 3rd quadrant. So, it is not sufficient.

(2) implies that x> 0, since a>0 in order to satisfy the criteria. Since we don’t know about y, we can not say whether (x,y) lies in the same quadrant as (-a,b) and (-b,a).

Combining these two, (x,y) is in the 1st quadrant. So, it is not in the same quadrant as (-a,b) and (-b,a). So, answer is (C)

I have attached the solution for better clarification. Hope this helps.