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Q.
Point $R(h, k)$ divides a line segment between the axes in the ratio $1:2$. Find the equation of the line,
Straight Lines
Solution:
Let equation of line $AB$ is $\frac{x}{a}+\frac{y}{b}=1\quad\ldots\left(i\right)$
A point $R\left(h, k\right)$ divides the line $AB$ in the ratio $1 : 2$.
Now, $R\left(h, k\right)=\left(\frac{1x_{2}+2x_{1}}{1+2}, \frac{1y_{2}+2y_{1}}{1+2}\right)$
$\Rightarrow h=\frac{\left(1 \times 0\right)+\left(2 \times a\right)}{1+2}, k=\frac{\left(1 \times b\right)+\left(2 \times 0\right)}{1+2}$
$\Rightarrow h=\frac{2a}{3}$, $k=\frac{b}{3}$
$\Rightarrow a=\frac{3h}{2}$, $b=3k$
On putting the values of $a$ and $b$ in $\left(i\right)$, we get
