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Ans: FOURTH QUADRANT
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Answer:
Here point 'P' divides the segment joining point 'A'(7,-6) & point 'B'(3,4)
(1): If AP:BP = 1:2 , then the point P lies in the 4th quadrant.
(2): If BP:AP = 1:2, then the point P lies in the 1st quadrant.
We can get the division point P by section formula
If AP:BP = 1:2
=> X = (3 + 14)/3= 17/3
Y = (4+ -12)/3 = -8/3
& ( +, -) lies in 4th quadrant
Now, if BP:AP = 1:2
=> X = (7+6)/3 = 13/3
Y = (-6+8)/3 = 2/3
Since both coordinates are positive (+,+). So P in this case lies in 1st quadrant.
But now the point to be noted is , point (7,-6) is mentioned at first place & antecedent of the ratio(1:2) is 1. So in this case we may consider AP:BP = 1:2 & in such case division point lies in 4th quadrant