# 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

**Solution:**

The coordinates of the point P(x, y) which divides the line segment joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}), internally, in the ratio m_{1}: m_{2} is given by the Section Formula: P(x, y) = [(mx_{2} + nx_{1 }/ m + n)] , [(my_{2} + ny_{1 }/ m + n)]

Let the ratio be k : 1

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

By using the Section formula,

P (x, y) = [mx_{2} + nx_{1 }/ m + n] , [my_{2} + ny_{1 }/ m + n]

Therefore, the coordinates of the point of division is

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

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

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

⇒ 5k = 5 (By cross multiplying & Transposing)

k = 1

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

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

= [(- 4 + 1) / 2, (5 - 5) / 2]

= [- 3 / 2, 0]

**Video Solution:**

## 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

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.2 Question 5:

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

The ratio in which the line segment joining A (1, - 5) and B (- 4, 5) is divided by the x-axis is 1:1 and the point that divides is (-3/2, 0)