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In what ratio does the X-axis divides the line segment joining the points$(2, -3)$ and $(5, 6)$? Also, find the coordinates of the point of intersection.
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Let the co ordinate of the point of intersection be $(x, 0)$.
Let ratio be $k:1$
$\frac{6k-3}{k+1} = 0$
$\Rightarrow k = \frac{1}{2}$
$\therefore$ required ratio is $1: 2$
$x = \frac{5\times1+2\times2}{1+2} = \frac{9}{3} = 3$
$\therefore$ the co ordinate of the point of intersection is $(3,0)$
Let ratio be $k:1$
$\frac{6k-3}{k+1} = 0$
$\Rightarrow k = \frac{1}{2}$
$\therefore$ required ratio is $1: 2$
$x = \frac{5\times1+2\times2}{1+2} = \frac{9}{3} = 3$
$\therefore$ the co ordinate of the point of intersection is $(3,0)$