Question

Find coordinates of a point that divides the line joining the points $(1,3)$ and $(2,7)$ in the ratio $3:4$.

Answer 1

Section formula :
Any point let say $(x,y)$ divides the line joining points $(x_1,y_1)$ & $(x_2,y_2)$ in the ratio $m:n$ then co-ordinates were given by the formula
$x=\frac{x_1\times n+x_2\times m}{m+n}$
$y=\frac{y_1\times n+y_2\times m}{m+n}$
Let a point $P$ divides the line joining the points $(1,3)$ & $(2,7)$ in the ratio $m:n$
The co-ordinates of point P is given by
$P=(\frac{1\times n+2\times m}{m+n},\frac{3\times n+7\times m}{m+n})$

Given that $m:n=3:4.$
$\Rightarrow P=(\frac{1\times 4+2\times 3}{3+4},\frac{3\times 4+7\times 3}{3+4})$
$\Rightarrow P=(\frac{10}{7},\frac{33}{7})$
So, co-ordinates of point $P$ which divides the line joining the points $(1,3)$ and $(2,7)$ in the ratio $3:4$ is $P(\frac{10}{7},\frac{33}{7}).$