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# Find the ratio in which the line segment joining A (1, – 5) and B (- 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

Let p(x , 0) be the point which devides the line segment joining A(1, -5 ) and B(-4,5 ) in the ratio m : 1

Then the using section formula

(x , 0 ) = $$( \frac{m×(-4) + 1 × 1 }{m+1} , \frac{m×5+1×(-5)}{m+1} )$$
$$\Rightarrow 0 = \frac{m×5+1×(-5)}{m+1}$$
$$\Rightarrow 0 = 5m - 5$$
$$\Rightarrow m = 5 /5 = 1$$

Hence the required ratio is 1 : 1

Since the ratio is 1 : 1 , so P is the mid point

$$\therefore$$ x = $$\frac{m×(-4) + 1 × 1 }{m+1}$$
x = $$\frac{1×(-4) + 1 × 1 }{1+1} = \frac{-4+1}{2} = \frac{-3}{2}$$

$$\therefore ( \frac{-3}{2} , 0 )$$ is the required point