Question

Determine the ratio in which the straight line $x-y-2=0$ divides the line segment joining $(3,-1)$ and $(8,9)$

Answer 1

Let the ratio be $m:n$

Here, $x_1=3,y_1=-1$ and $x_2=8,y_2=9$

$\therefore$ By using section formula :

$(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

$=(\frac{8m+3n}{m+n},\frac{9m-n}{m+n})$

Now, Given straight line is $x-y-2=0$

$\Rightarrow$ We can substitute $x=$ $\frac{8m+3n}{m+n}$ and $y=$ $\frac{9m-n}{m+n}$ as this point lies on the given line.

$\therefore \frac{8m+3n}{m+n}-\frac{9m-n}{m+n}-2=0$

$\Rightarrow 8m+3n-9m+n-2m-2n=0$

$\Rightarrow -3m+2n=0$

$3m=2n$

$\Rightarrow \frac{m}{n}=\frac{2}{3}$

$\Rightarrow m:n=2:3$ internally.