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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.

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#### 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 is

`((-4k+1)/(k+1),(5k-5)/(k+1))`

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

`:.(5k-5)/(k+1) =1`

k =1

Therefore, *x*-axis divides it in the ratio 1:1.

Division point = `((-4(1)+1)/(1+1), (5(1)-5)/(1+1)) = ((-4+1)/2, (5-5)/2) =((-3)/2, 0)`

Concept: Section Formula

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