$\mathrm{A}(2, 3), \mathrm{B}(\mathrm{x}, \mathrm{y})$ and if $C\left(3, 4\right)$ divides $\mathrm{AB}$ in the ratio $1 : 5$ internally then $\mathrm{B}=$

$$\begin{gathered} \mathrm{A}=(2, 3), \mathrm{B}=(\mathrm{x}, \mathrm{y}), \mathrm{C}=(3, 4), \mathrm{m}:\mathrm{n}=1:5 \\ \mathrm{C}=\left[\frac{1\left(\mathrm{x}\right)+5\left(2\right)}{6}, \frac{1\left(\mathrm{y}\right)+5\left(3\right)}{6}\right] \\ \Rightarrow [3, 4]=\left[\frac{\mathrm{x}+10}{6}, \frac{\mathrm{y}+15}{6}\right] \\ \Rightarrow 3=\frac{\mathrm{x}+10}{6}, 4=\frac{y+15}{6} \\ \Rightarrow \mathrm{x}+10=18, \mathrm{y}+15=24 \\ \Rightarrow \mathrm{x}=8, \mathrm{y}=9 \\ \therefore \mathrm{B}=(8, 9) \end{gathered}$$