# Determine the ratio in which the line 3x+y-9=0 divides the segment joining the point (1,3) and (2,7)

Solution: Suppose the line 3x+y-9=0 divides the line segment joining A(1,3) and b(2,7) in the ratio k:1 at point C.then the coordinate of C are

$\\ (2k+1/k+1,7k+3/k+1)\\ \\$

but, C lies on 3x+y-9=0 . Therefore ,

$\\3(2k+1/k+1)+7k+3/k+1 -9=0\\ \\\Rightarrow 6k+3+7k+3-9k-9=0\\ \\\Rightarrow k=3/4$

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