Question

Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) and B(1, 2). Also find k.

Answer 1

Let the ratio be x : 1.
Using the section formula,
$$\begin{gathered} k=\frac{1x+1\times 8}{x+1} \\ \Rightarrow kx+k=x+8.....\left(1\right) \\ \mathrm{Also},7=\frac{2x+9}{x+1} \\ \Rightarrow 7x+7=2x+9 \\ \Rightarrow 5x=2 \\ \Rightarrow x=\frac{2}{5} \end{gathered}$$
So, the required ratio is 2 : 5.
Putting this value of x in (1) we get
$$\begin{gathered} k\left(\frac{2}{5}+1\right)=\frac{2}{5}+8 \\ \Rightarrow \frac{7}{5}k=\frac{42}{5} \\ \Rightarrow k=6 \end{gathered}$$