Write the coordinates of the point dividing line segment

Let $P(x, y)$ be the point which divide the line segment joining $A(2,3)$ and $B(3,4)$ in the ratio $1: 5$.

Now according to the section formula if point a point $\mathrm{P}$ divides a line segment joining $\mathrm{A}\left(x_{1}, y_{1}\right)$ and $\mathrm{B}\left(x_{2}, y_{2}\right)$ in the ratio $\mathrm{m}$ : $\mathrm{n}$ internally than,

$\mathrm{P}(x, y)=\left(\frac{n x_{1}+m x_{2}}{m+n}, \frac{m y_{1}+m y_{2}}{m+n}\right)$

Now we will use section formula as,

$\mathrm{P}(x, y)=\left(\frac{5(2)+3}{5+1}, \frac{5(3)+4}{5+1}\right)$

$=\left(\frac{13}{6}, \frac{19}{6}\right)$

So co-ordinate of $P$ is

$\left(\frac{13}{6}, \frac{19}{6}\right)$