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Find the coordinates of the point C which lies on the line AB produced such that $AC = 2BC$, where coordinates of points A and B are $(-1, 7)$ and $(4,-3)$ respectively.
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A $(-1, 7)$ B $(4, -3)$ C $(x, y)$
Let coordinates of point C be $(x, y)$
$AC = 2 BC$
$\Rightarrow$ B is mid-point of AC
$\Rightarrow \frac{-1+x}{2} = 4 \Rightarrow x = 9$
$\frac{7+y}{2} = -3 \Rightarrow y = -13$
$\therefore$ Coordinates of C are $(9, -13)$
Let coordinates of point C be $(x, y)$
$AC = 2 BC$
$\Rightarrow$ B is mid-point of AC
$\Rightarrow \frac{-1+x}{2} = 4 \Rightarrow x = 9$
$\frac{7+y}{2} = -3 \Rightarrow y = -13$
$\therefore$ Coordinates of C are $(9, -13)$