Question

Point R(h, k) divides a line segment between the axis in the ratio 1: 2. Find equation of the line.

Answer 1

Let A(x, 0) and B(0, y) be two points where the line interest x and y axis respectively and R(h, k) is a point divides AB in the ratio 1 : 2.

Then $\frac{2x+0}{2+1}=h$ and $\frac{0+y}{2+1}=k$

$\Rightarrow x=\frac{3}{2}h$ and y = 3k

Now equation of required line is

$\frac{x}{\frac{3}{2}h}+\frac{y}{3k}=1\Rightarrow \frac{2x}{3h}+\frac{y}{3k}=1$

$\Rightarrow$ 2kx + hy = 3kh