Question

Find the coordinates of the point which divides the line joining the points $(1,3)$ and $(2,7)$ in the ratio $3:4$.

Answer 1

If a points divides line joining two points $(a,b)$ and $(c,d)$ in ratio $m:n$ then its coordinates are $(\frac{mc+na}{m+n},\frac{md+nb}{m+n})$

Let the point be $P(h,k)$

$(1,3)$ and $(2,7)$ is divided by $(h,k)$ in $(3:4)$ then

$h=\frac{3\left(2\right)+4\left(1\right)}{3+4}=\frac{10}{7}k=\frac{3\left(7\right)+4\left(3\right)}{7}=\frac{33}{7}$

So, the coordinates of the point are $(\frac{10}{7},\frac{33}{7})$