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Question

The ratio in which the line joining A(4,2) and B(3,6) is divided by point P(x,3) is k. Then 9k=?

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Solution

Let P(x,3) divide the line segment joining the points A(4,2) and B(3,6) in the ratio k:1
Coordinates of P is (m1x2+m2x1m1+m2,m1y2+m2y1m1+m2)=(3k4k+1,6k+2k+1)
But coordinate of P is (x,3)
6k+2k+1=3
6k+2=3k+3
3k=1k=13
The required ratio is 13:1 i.e., 1:3 (internally)
x=3k4k+1
Putting k=13, we get
x=3×13413+1=141+33=34/3=94

9k=3

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