# Find the coordinates of the points of trisection of the line segment joining (4, - 1) and (- 2, - 3)

**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.

Let the points be A(4, - 1) and B(- 2, - 3).

Let P (x_{1}, y_{1}) and Q (x_{2}, y_{2}) be the points of trisection of the line segment joining the given points. Then, AP = PQ = QB

By Section formula

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

Therefore, by observation point P divides AB internally in the ratio 1 : 2.

Hence m : n = 1 : 2

By substituting the values in the Equation (1)

x_{1} = [1 × (- 2) + 2 × 4] / (1 + 2)

x_{1} = (- 2 + 8) / 3

= 2

y_{1} = [1 × (- 3) + 2 × (- 1)] / (1 + 2)

y_{1} = (- 3 - 2) / (1 + 2)

= - 5/3

Hence, P(x_{1} , y_{1}) = (2, - 5 / 3)

Therefore, by observation point Q divides AB internally in the ratio 2 : 1.

Hence m : n = 2 : 1

By substituting the values in the Equation (1)

x_{2} = [2 × (- 2) + 1 × 4] / (2 + 1)

= (- 4 + 4) / 3

= 0

y_{2} = [2 × (- 3) + 1 × (- 1)] / (2 + 1)

= (- 6 - 1) / 3

= - 7/3

Therefore, Q (x_{2} , y_{2}) = (0, - 7 / 3)

Hence, the points of trisection are P(x_{1} , y_{1}) = (2, - 5 / 3) and Q (x_{2} , y_{2}) = (0, - 7 / 3)

**Video Solution:**

## Find the coordinates of the points of trisection of the line segment joining (4, - 1) and (- 2, - 3)

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.2 Question 2:

Find the coordinates of the points of trisection of the line segment joining (4, - 1) and (- 2, - 3)

The coordinates of the points of trisection of the line segment joining (4, - 1) and (- 2, - 3) are (2, - 5 / 3) and (0, - 7 / 3)