Question

Find the co-ordinates of points which divides the line segment joining the points $(-2,5)$ and $(6,8)$ in the ratio $3:2$ 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 required point.

Given that the point $(h,k)$ divides the line segment joining the points $(-2,5)$ and $(6,8)$ in the ratio $3:2$ internally.

Therefore,

$(h,k)=(\frac{-2\times 2+6\times 3}{3+2},\frac{5\times 2+8\times 3}{3+2})$

$\Rightarrow (h,k)=(\frac{-4+18}{5},\frac{10+24}{5})$

$\Rightarrow (h,k)=(\frac{14}{5},\frac{34}{5})$

Hence the coordinate of required point are $(\frac{14}{5},\frac{34}{5})$.