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A point $P$ divides the line segment joining the points $A(-3, 5)$ and
n$B(7, -4)$ in a certain ratio. If the point $P$ lies on the line $y = 2x$, then find
nthe ratio $AP: PB$ and coordinates of point $P$.
n$B(7, -4)$ in a certain ratio. If the point $P$ lies on the line $y = 2x$, then find
nthe ratio $AP: PB$ and coordinates of point $P$.
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Let $AP: PB = k : 1$
Coordinates of point $P$ are $(\frac{7k-3}{k+1}, \frac{-4k+5}{k+1})$ (1/2 Mark)
Since point $P$ lies on the line $y = 2x$
Therefore, $\frac{-4k+5}{k+1} = 2 \times \frac{7k-3}{k+1}$ (1/2 Mark)
$\Rightarrow k = \frac{11}{18}$ (1/2 Mark)
$\therefore AP : PB = 11:18$ (1/2 Mark)
Coordinates of $P$ are $(\frac{7\times11-3\times18}{11+18}, \frac{-4\times11+5\times18}{11+18}) = (\frac{23}{29}, \frac{46}{29})$ (1 Mark)
Coordinates of point $P$ are $(\frac{7k-3}{k+1}, \frac{-4k+5}{k+1})$ (1/2 Mark)
Since point $P$ lies on the line $y = 2x$
Therefore, $\frac{-4k+5}{k+1} = 2 \times \frac{7k-3}{k+1}$ (1/2 Mark)
$\Rightarrow k = \frac{11}{18}$ (1/2 Mark)
$\therefore AP : PB = 11:18$ (1/2 Mark)
Coordinates of $P$ are $(\frac{7\times11-3\times18}{11+18}, \frac{-4\times11+5\times18}{11+18}) = (\frac{23}{29}, \frac{46}{29})$ (1 Mark)