Question

A and B are the points $(1,2)$ and $(2,3)$. Find the coordinates of point C on the line segment ABC such that $3AC=4BC$.

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

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

Since, $3AC=4BC$

$\therefore$ $C$ divides $AB$ in ratio $4:3$

$x=\frac{8+3}{7}=\frac{11}{7},andy=\frac{12+6}{7}=\frac{18}{7}$