Question

In what ratio does the point $(\frac{1}{2},6)$ divide the line segment joining the points $(3,5)$ and $(-7,9)$ ?

Answer 1

We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is

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

$\therefore \frac{-7m+3n}{m+n}=\frac{1}{2}$ & $\frac{9m+5n}{m+n}=6$

$-14m+6n=m+n$ & $9m+5n=6m+6n$

$\Rightarrow 5n=15m$ $3m=n$

$\therefore \frac{m}{n}=\frac{5}{15}=\frac{1}{3}\Rightarrow 1:3$