Question

Find the coordinate of point P which divides the join of $A(6,5)$ and $B(9,2)$ in the ratio $1:2$ 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 $P=(x,y)$

Therefore, we have

$x=\frac{9+12}{3}=3+4=7$

$y=\frac{2+10}{3}=4$

$\therefore$ $P=(7,4)$