Question

Determine the ratio in which the line 3 + − 9 = 0 divides the line segment joining the points (1, 3) and (2, 7).

Answer 1

i think you meant 3x+ y- 9=0

if then the answer is

Let the point (x,y) divides AB in the ratio k:1.

 

By section formula,

x = (2k+1)/(k+1)  ,  y = (7k+3)/(k+1)

 

Now, this point also lies on the given line so it would satisfy the equation 3x+y-9=0

Therefore,

3(2k+1) + (7k+3) -9(k+1) = 0

k = 3/4

Hence, the required ratio is 3:4.