Question

Determine the ratio in which the point $P(3,5)$ divides the join of $A(1,3)$ and $B(7,9)$.

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

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

Therefore, we have

$\frac{7\times m+n}{m+n}=3$

$7m+n=3m+3n$

$4m=2n$

$\frac{m}{n}=\frac{1}{2}$