A point $\displaystyle \mathrm{P}(\mathrm{x}, 7)$ divides a line segment joining the points $\displaystyle \mathrm{A}(-5,4)$ and B$\displaystyle (7, 9)$ in a certain ratio. Find the ratio and hence find the value of x.

Let \(\displaystyle \mathrm{AP}: \mathrm{PB}=\mathrm{k}: 1\) \(\displaystyle \therefore 7=\frac{9 \mathrm{k}+4}{\mathrm{k}+1} \Rightarrow \mathrm{k}=\frac{3}{2}\) So, required ratio is $\displaystyle 3$ : $\displaystyle 2$ Hence, \(\displaystyle \mathrm{x}=\frac{7 \times 3+(-5) \times 2}{3+2}=\frac{11}{5}\)