Question

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

Answer 1

Let the required ratio be $k:1$. Let $P(x,y)$ be the point on the given line dividing AB in the ratio $k:1$.

Using section formula,

$x=\frac{3k+2}{k+1}$ and $y=\frac{7k-2}{k+1}$

This point $P(x,y)$ lies on the line $2x+y-4=0$, thus it will satisfy the given equation of line.

Therefore,

$2\times \frac{3k+2}{k+1}+\frac{7k-2}{k+1}=4$

$9k=2$

$k=\frac{2}{9}$

Therefore, the required ratio is $\frac{2}{9}:1$ or $2:9$.