Question

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

Answer 1

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