Question

The point which divides the line joining the points $(1,3)$ and $(2,7)$ in the ratio $3:4$ is

Answer 1

Let P be the required point.

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

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

Since, $m:n=3:4$

Therefore, we have

$P=\frac{6+4}{3+4},\frac{21+12}{3+4}$

$P=\frac{10}{7},\frac{33}{7}$