Question

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

Answer 1

suppose the line 3x+y-9=0 divides the line sebment joining A(1,3) and B(2,7) in the ratio k:1 at point C. then the coordinates of C are
{2k+1  , 7k+3}
   k+1      k+1
but, C lies on 3x+y-9=0. therefore
3{2k+1 }+ 7k+3    -9=0 => 6k+3+7k+3-9k-9=0 => k=3/4
     hence ratio be 3:4