Question

Given a line segment $AB$ joining the points $A(-4,6)$ and $(8,-3)$. Find
find the ratio in which $AB$ is divided by the y-axis.

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

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

Let this point divides the segment in $m:n$ and we know the point on y-axis has $x$ coordinate $0$, then

$\frac{8m-4n}{m+n}=0$

$8m=4n$
$\frac{m}{n}=\frac{4}{8}$

$m:n=1:2.$