Question

find the ratio in which the point P(11/6, 17/6) divides the line segment joining A(1,2) and B(3,4)

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{ratio}\mathrm{be}\mathrm{\lambda }:1 \\ \mathrm{Given} \\ \mathrm{A}(1,2)\mathrm{and}\mathrm{B}(3,4) \\ \mathrm{From}\mathrm{the}\mathrm{given}\mathrm{data} \\ \left(\frac{11}{6},\frac{17}{6}\right)=\left(\frac{3\left(\mathrm{\lambda }\right)+1\left(1\right)}{\mathrm{\lambda }+1},\frac{4\left(\lambda \right)+1\left(2\right)}{\lambda +1}\right) \\ \Rightarrow \frac{3\mathrm{\lambda }+1}{\mathrm{\lambda }+1}=\frac{11}{6} \\ \Rightarrow 18\mathrm{\lambda }+6=11\mathrm{\lambda }+11 \\ \Rightarrow 7\mathrm{\lambda }=5 \\ \Rightarrow \mathrm{\lambda }=\frac{5}{7} \\ \therefore \mathrm{Required}\mathrm{ratio}\mathrm{is}5:7 \end{gathered}$$