Question

Find the coordinates of the point which divides the join of $(-1,7)$ and $(4,-3)$ in the ratio $2:3$.

Answer 1

If a pont $P(x,y)$ divides the line segment joining the points $(-1,7)$ and $(4,-3)$ in the ratio $m_1$ and $m_2$ then

$x=\frac{m_1{x}_2+m_2{x}_1}{m_1+m_2}$

And

$y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$

Here $m_1=2,m_2=3,x_1=-1,x_2=4$

$\Rightarrow x=\frac{2\times 4+3\times (-1)}{2+3}$

$\Rightarrow x=\frac{8-3}{5}=\frac{5}{5}=1$

and $y=\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2}$

Here $y_1=7,y_2=-3$

$\Rightarrow y=\frac{2\times (-3)+3\times 7}{2+3}$

$\Rightarrow y=\frac{-6+21}{5}=\frac{15}{5}=3$

$\therefore P=(1,3)$