Question

The coordinates of the point which divides the line segment joining the points $(6,3)and(-4,5)$ in the ratio $3:2$ Internally is $(0,\frac{k}{5})$. Find k

Answer 1

Using the section formula, if a
point $(x,y)$ divides the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ internally in the ratio $m:n$, then
$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$
Substituting $(x_1,y_1)=(6,3)$ and $(x_2,y_2)=(-4,5)$ and $m=3,n=2$ in the section formula, we get
the point P $=(\frac{3(-4)+2\left(6\right)}{3+2},\frac{3\left(5\right)+2\left(3\right)}{3+2})=(0,\frac{21}{5})$