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.

Asked by Abhisek | 1 year ago |  99

Solution :-

Let the ratio in which the line segment joining A (1, – 5) and B ( – 4, 5) is divided by x-axis be k : 1.

Therefore, the coordinates of the point of division, say P(x, y) is

$$\dfrac{(-4k+1)}{(k+1)}\,\dfrac{(5k-5)}{(k+1)}$$

or  P(x, y)= $$\dfrac{-4k+1}{k+1},\dfrac{5k-5}{k+1}$$

We know that y-coordinate of any point on x-axis is 0.

Therefore, $$\dfrac{5k-5}{k+1}=0$$

5k = 5

or k = 1

So, x-axis divides the line segment in the ratio 1:1.

Now, find the coordinates of the point of division:

P (x, y) = $$\dfrac{(-4(1)+1)}{(1+1) },\dfrac{(5(1)-5)}{(1+1)}=\dfrac{-3}{2},0$$

Answered by Pragya Singh | 1 year ago

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