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In what ratio does the x-axis divide the line segment joining the points (2, –3) and (5, 6)? Also, find the coordinates of the point of intersection.

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#### Solution

Let the required ratio be λ : 1. Then, the coordinates of the point of division are,

`R( \frac{5\lambda +2}{\lambda +1},\ \frac{6\lambda -3}{\lambda +1})`

But, it is a point on x-axis on which y-coordinates of every point is zero.

`\therefore \frac{6\lambda -3}{\lambda +1}=0`

`\Rightarrow \lambda =\frac{1}{2}`

Thus, the required ratio is 1/2 : 1 or 1 : 2

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