Find the ratio in which the y-axis divides the line segment joining the points 𝐴(5, − 6) and 𝐵(− 1, − 4). Also find the coordinates of the point of division.

Let the point be 𝐴(5, − 6), 𝐵(− 1, − 4) and 𝑃(0, 𝑦). 

Point 𝑃 is on y-axis ,hence its x coordinate is 0. 

So, it is of the form 𝑃(0, 𝑦)

Let the ratio be 𝑘: 1

Where $m_1=k,m_2=1,x_1=5,x_2=-1,y_1=-6,y_2=-4,x=0,y=0$

Using section formula

$$\begin{gathered} \begin{array}{r}x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}\\ 0=\frac{-k+5}{k+1}\end{array} \\ k =5 \end{gathered}$$

Also, 

$\begin{array}{r}y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}\\ 0=\frac{-4k-6}{k+1}\\ 0=\frac{-20-6}{6}\\ =\frac{-13}{3}\end{array}$

Hence the coordinate of point is  $P\left(0,\frac{-13}{3}\right)$