Question

Find the ratio in which line segment joining the ponts $(-3,10)$ and $(6,-8)$ is divided by $(-1,6)$.

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 the ratio be $m:n$

Therefore, we have

$(-1,6)=(\frac{m6+n(-3)}{m+n},\frac{-m8+10n}{m+n})$

$0=7m-2n\&-14m+4n=0=>\frac{m}{n}=\frac{2}{7}=>m:n::2:7$