Question

Find the co-ordinates of the point which divides the line segment joining points $(1,-3)$ and $(-3,9)$ in the ratio $1:3$ internally.

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

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

Let $(h,k)$ be the point which divides the line segment joining points $(1,-3)$ and $(-3,9)$ in the ratio $1:3$ internally.

By section formula,

$(h,k)=(\frac{1\times 3+1\times (-3)}{3+1},\frac{-3\times 3+9\times 1}{1+3})=(0,0)$

Hence the origin divides the line segment joining points $(1,-3)$ and $(-3,9)$ in the ratio $1:3$ internally.