If P (9a – 2, –b) divides line segments joining A (3a + 1, –3) and B (8a, 5) in the ratio 3 : 1, find the values of a and b

Solution:

Given, point P(9a - 2, -b) divides the line segments joining A(3a + 1, -3) and B(8a, 5) in the ratio 3:1

We have to find the values of a and b.

The coordinates of the point P which divides the line segment joining the points A (x₁ , y₁) and B (x₂ , y₂) internally in the ratio m₁ : m₂ are

[(m₁x₂ + m₂x₁)/(m₁ + m₂) , (m₁y₂ + m₂y₁)/(m₁ + m₂)]

Here, m₁:m₂ = 3:1, (x₁ , y₁) = (3a + 1, -3) and (x₂ , y₂) = (8a, 5)

So, [(3(8a) + 1(3a + 1))/(3 + 1), (3(5) + 1(-3))/(3 + 1)] = (9a - 2, -b)

[(24a + 3a + 1)/4, (15 - 3)/4] = (9a - 2, -b)

[(27a + 1)/4, 12/4] = (9a - 2, -b)

Now, (27a + 1)/4 = 9a - 2

27a + 1 = 4(9a - 2)

27a + 1 = 36a - 8

36a - 27a = 1 + 8

9a = 9

a = 9/9

a = 1

Also, -b = 12/4

-b = 3

b = -3

Therefore, the values of a and b are 1 and -3.

✦ Try This: Determine the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A (2, - 2) and B (3, 7)

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

NCERT Exemplar Class 10 Maths Exercise 7.3 Problem 12

Summary:

If P (9a – 2, –b) divides line segments joining A (3a + 1, –3) and B (8a, 5) in the ratio 3 : 1, the values of a and b are 1 and -3 respectively

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