Question

Find the ratio in which the $Y$ axis divides the line segment joining the points $(5,-6)$ and $(-1,-4)$.

Answer 1

Using the section formula, if a point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$, then

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

Since the line segment divided by $Y$-axis.

So, the point is $(0,y)$.

$A(5,-6)$ and $B(-1,-4)$

Now let ratio be $m:n$

$\Rightarrow (0,y)=(\frac{m5+(-n)}{m+n},\frac{-6m-4n}{m+n})$

$\Rightarrow (0,y)=(\frac{5m-n}{m+n},\frac{-6m-4n}{m+n})$

Lets compare the corresponding coordinates,

$\frac{5m-n}{m+n}=0$

$\Rightarrow 5m-n=0$

$\Rightarrow 5m=n$

$\Rightarrow \frac{m}{n}=\frac{1}{5}$

$\Rightarrow m:n=1:5$

Hence, the required ratio is $1:5$.