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A point P$(x, 7)$ divides a line segment joining the points A$(-5, 4)$ and B$(7, 9)$ in a certain ratio. Find the ratio and hence find the value of $x$.
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Sol. Let AP : PB $= k : 1$ (1/2 Mark)
$\therefore 7 = \frac{9k + 4}{k+1} \Rightarrow k = \frac{3}{2}$ (1 Mark)
So, required ratio is $3 : 2$ (1/2 Mark)
Hence, $x = \frac{7\times3+(-5)\times2}{3+2} = \frac{11}{5}$ (1 Mark)
$\therefore 7 = \frac{9k + 4}{k+1} \Rightarrow k = \frac{3}{2}$ (1 Mark)
So, required ratio is $3 : 2$ (1/2 Mark)
Hence, $x = \frac{7\times3+(-5)\times2}{3+2} = \frac{11}{5}$ (1 Mark)