Question

Find the coordinates of the point P which divides segment JL externally in the ratio m:n in the following examples.
(i) J(4,-5), L(-6, 7), m:n = 3:5

Answer 1

$$\begin{gathered} \mathrm{Given}:\mathrm{J}\equiv \left(4,-5\right)\mathrm{and}\mathrm{L}\equiv \left(-6,7\right) \\ \mathrm{Here},x_1=4,y_1=-5,x_2=-6\mathrm{and}{y}_2=7. \\ \mathrm{And}m=3\mathrm{and}n=5. \\ \mathrm{Let}\mathrm{P}\equiv \left(x,y\right)\mathrm{divide}\mathrm{JL}\mathrm{externally}. \\ \mathrm{By}\mathrm{section}\mathrm{formula}\mathrm{for}\mathrm{external}\mathrm{division}, \end{gathered}$$

$$\begin{gathered} x=\frac{m{x}_2-n{x}_1}{m-n} \\ \Rightarrow x=\frac{3\times \left(-6\right)-5\times 4}{3-5} \\ \Rightarrow x=\frac{-18-20}{-2} \\ \therefore x=19 \end{gathered}$$ $$\begin{gathered} y=\frac{m{y}_2-n{y}_1}{m-n} \\ \Rightarrow y=\frac{3\times 7-5\times \left(-5\right)}{3-5} \\ \Rightarrow y=\frac{21+25}{-2} \\ \therefore y=-23 \end{gathered}$$

$\therefore \text{C}\mathrm{oordinate}\text{s}\mathrm{of}\mathrm{point}\mathrm{P}\equiv \left(19,-23\right)$