Question

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

Answer 1

Let the given line divide the line segments joining the two points (1,3) and (2,7) in ratio k:1 at the point P.          Coordinate s of P are (k*2+1*1/k+1,k*7+1*3/k+1).                  According to problem,.                        3*(2k+1/k+1)+(7k+3/k+1)=9.                       =>3(2k+1)+7k+3=9(k+1).                              =>6k+3+7k+3-9k-1=0.                                =>4k-5=0.                                                   =>k=5/4.                                              Required ratio is 5:4 (ans).