Question

In what ratio is the joining the points
$(3,-6)$ and $(-6,8)$ 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

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

Given points $(3,-6),(-6,8)$

Let y-axis divide it in ratio $k:1$

Now k-coordinate is zero

$0=\frac{-6k+3}{k+1}$

$6k=3$

$k=\frac{1}{2}$

$\therefore$ y-axis divide it in ratio $1:2$.