Question

Find the coordinate of point which divides $A(5,6)$ and $(5,10)$ in $2:3$.

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 coordinate of the point is $(x,y)$.

By section formula, we have

$x=\frac{15+10}{5}=5$ and

$y=\frac{18+20}{5}=\frac{38}{5}$.

Hence required point is $(5,\frac{38}{5}$)