90
Find the ratio in which the x-axis divides the line segment joining the points $(-6, 5)$ and $(-4, -1)$. Also, find the point of intersection.
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Let coordinates of $P$ be $(x, 0)$ and $P$ divides the line segement $AB$ in the ratio $k: 1$ (I) (1/2 Mark)
$(\frac{-4k-6}{k+1}, \frac{-k+5}{k+1}) = (x, 0)$ (II) (1 Mark)
$\frac{-k+5}{k+1} = 0 \Rightarrow k = 5$ (III) (1/2 Mark)
Hence the required ratio is $5: 1$ (IV) (1/2 Mark)
$\therefore$ Coordinates of $P$ are $(\frac{-4\times5-6}{5+1}, 0) = (\frac{-13}{3}, 0)$ (V) (1/2 Mark)
$(\frac{-4k-6}{k+1}, \frac{-k+5}{k+1}) = (x, 0)$ (II) (1 Mark)
$\frac{-k+5}{k+1} = 0 \Rightarrow k = 5$ (III) (1/2 Mark)
Hence the required ratio is $5: 1$ (IV) (1/2 Mark)
$\therefore$ Coordinates of $P$ are $(\frac{-4\times5-6}{5+1}, 0) = (\frac{-13}{3}, 0)$ (V) (1/2 Mark)