What are the coordinates of the points of trisection of the line segment joining the points?

Solution:

The coordinates of the point P(x, y) which divides the line segment joining the points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁: m₂ is given by the section formula.

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

Let P (x₁, y₁) and Q (x₂, y₂) be the points of trisection of the line segment joining the given points.

Then, AP = PC = CB

By Section formula ,

P(x, y) = [(mx₂ + nx₁) / (m + n), (my₂ + ny₁) / (m + n)] ...... (1)

Considering A(4, - 1) and B(- 2, - 3), by observation point P(x₁, y₁) divides AB internally in the ratio 1 : 2.

Hence m : n = 1 : 2

By substituting the values in the Equation (1)

x₁ = [1 × (- 2) + 2 × 4] / (1 + 2)

x₁ = (- 2 + 8) / 3

= 2

y₁ = [1 × (- 3) + 2 × (- 1)] / (1 + 2)

y₁ = (- 3 - 2) / (1 + 2)

= - 5/3

Hence, P(x₁ , y₁) = (2, - 5/3)

Now considering A(4, - 1) and B(- 2, - 3), by observation point C(x₂, y₂) divides AB internally in the ratio 2 : 1.

Hence m : n = 2 : 1

By substituting the values in the Equation (1)

x₂ = [2 × (- 2) + 1 × 4] / (2 + 1)

= (- 4 + 4) / 3

= 0

y₂ =  [2 × (- 3) + 1 × (- 1)] / (2 + 1)

= (- 6 - 1) / 3

= - 7/3

Therefore, C(x₂ , y₂) = (0, - 7/3)

Hence, the points of trisection are P(x₁ , y₁) = (2, - 5/3) and C (x₂ , y₂) = (0, - 7/3)

☛ Check: NCERT Solutions Class 10 Maths Chapter 7

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

Summary:

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).

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