Question

Find the coordinates of the point which divides internally the join of the points
a) $(8,9)$ and $(-7,4)$ in the ratio $2:3$
b) $(1,-2)$ and $(4,7)$ in the ratio $1:2$.

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

$(x,y)=(\frac{m{x}_2+n{x}_1}{m+n},\frac{m{y}_2+n{y}_1}{m+n})$

(a) Let the point be $P(x,y)$

$(x,y)=(\frac{2\times -7+3\times 8}{2+3},\frac{2\times 4+3\times 9}{2+3})$

$X=2,Y==7$

So the point is $(2,7)$

(b) Let the required point be $P(x,y)$

Then,

$(x,y)=(\frac{1\times 4+2\times 1}{1+2},\frac{1\times 7+2\times -2}{1+2})$

$x=2,y=1$

therefore, required point $(2,1)$