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.

Explanation

Let the ratio be k : 1

Let the line segment be AB joining A (1, - 5) and B (- 4, 5)

By using the Section formula,

P (x, y) = [(mx₂ + nx₁) / m + n, (my₂ + ny₁) / m + n]

m = k, n = 1

Therefore, the coordinates of the point of division is

(x, 0) = [(- 4k + 1) / (k + 1), (5k - 5) / (k + 1)] ---------- (1)

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

Therefore, (5k - 5) / (k + 1) = 0

5k = 5

k = 1

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

To find the coordinates let's substitute the value of k in equation(1)

Required point = [(- 4(1) + 1) / (1 + 1), (5(1) - 5) / (1 + 1)]

= [(- 4 + 1) / 2, (5 - 5) / 2]

= [- 3/2, 0]