Question

Determine the ratio in which the line 2x+y-4 =0 divides the line segment joining the points A(2,-2) and B(3, 7).

Answer 1

Let us assume the line divides AB in k:1 ratio.
Coordinates of point of division can be given as follows:
$x=\frac{2+3k}{k+1}y=\frac{-2+7k}{k+1}$
Substituting the values of x and y in following equation;
Hence, the ratio is 2 : 9.
2x +y -4 =0
Or, $2\left(\frac{2+3k}{k+1}\right)+\left(\frac{-2+7k}{k+1}\right)-4=0$
Or, $\frac{4+6k}{k+1}+\left(\frac{-2+7k}{k+1}\right)=0$
Or, 4+6k-2+7k-4(k+1)=0
Or, 4+6k -2 +7k -4k -4 =0
Or, -2 +9k =0
Or, 9k =2
Or, $k=\frac{2}{9}$