Find the point P that internally divides the line segment connecting the points A(1,-3) and B(-3,9) in the ratio $1:3.$

Given the two points A(1,-3) and B(-3,9) and ratio $m: n=1: 3$.

Here apply the section formula, i. e. if a point $\mathrm{X}(\mathrm{x},\mathrm{y})$ divides the line segment $\mathrm{AB}$ joining the points $\text{A}\left({\text{x}}_1,{\text{y}}_1\right)\& \text{B}\left({\text{x}}_2,{\text{y}}_2\right)$ in the ratio $m:n$ then we have

$\therefore (x,y)=\left(\frac{3\times 1+1\times (-3)}{1+3},\frac{3\times (-3)+1\times 9}{1+3}\right)=(0,0)$