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Point P (5, –3) is one of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5). Is the following statement true or false

Solution:

Given, the line segment joining the points A(7, -2) and B(1, -5)

We have to check if the P(5, -3) is one of the two points of trisection of the line segment joining the given points.

By section formula,

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 k : 1 are [(kx₂ + x₁)/k + 1 , (ky₂ + y₁)/k + 1]

P(5, -3) divides the line segment A(7, -2) and B(1, -5) internally in the ratio k:1

So, (5, -3) = [k(1) + (7))/k + 1 , (k(-5) + (-2))/k + 1]

(5, -3) = [k + 7/k + 1, -5k - 2/k + 1]

Now, k + 7/k + 1 = 5

k + 7 = 5(k + 1)

k + 7 = 5k + 5

By grouping,

5k - k = 7 - 5

4k = 2

k = 2/4

k = 1/2

The point P(5, -3) divides the line segment AB in the ratio 1:2.

Therefore, point P is the point of trisection of AB.

✦ Try This: Determine if the point P (2, 4) is one of the two points of trisection of the line segment joining the points Q (6, 2) and R (1, -3).

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 9

Point P (5, - 3) is one of the two points of trisection of the line segment joining the points A (7, - 2) and B (1, - 5). Is the following statement true or false

Summary:

The statement “Point P (5, - 3) is one of the two points of trisection of the line segment joining the points A (7, - 2) and B (1, - 5)” is true as the point P divides the line segment AB internally in the ratio 1:2

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