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(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).
☛ Related Questions:
- To conduct Sports Day activities, in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along with AD, as shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segments joining the two flags, where should she post her flag?
- Find the ratio in which the line segment joining the points (- 3, 10) and (6, - 8) is divided by (- 1, 6).
- 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.
- If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.