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Question 15
The line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2 and it lies on the line 3x-18y+k=0. Find the value of k.

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Solution

Given that the line segment joining the points A(3,2) and B(5,1) is divided at the point P in the ratio 1:2.
Coordinate of point P{5(1)+3(2)1+2,1(1)+2(2)1+2}(5+63,1+43)(113,53)[By section formula, for internal ratio=(m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)]But the point P(113,53)lies on the line 3x-18y+k=0.3(113)18{53}+k=01130+k=0k19=0k=19Hence, the required value of k is 19.

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