Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, –5)

Solution:

Given, point P(3/4, 5/12) divides the line segment joining the points A(1/2, 3/2) and B(2, -5).

We have to find the ratio in which the point P divides the line segment AB.

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)]

Here, (x₁, y₁) = (1/2, 3/2) and (x₂, y₂) = (2, -5)

[(k(2) + (1/2))/(k + 1) , (k(-5) + (3/2))/(k + 1)] = (3/4, 5/12)

[(2k + (1/2))/(k + 1), (-5k + (3/2))/(k + 1)] = (3/4, 5/12)

Now, (2k + (1/2))/(k + 1) = 3/4

2k + (1/2) = 3/4(k + 1)

(4k + 1)/2 = (3k + 3)/4

4k + 1 = (3k + 3)/2

2(4k + 1) = 3k + 3

8k + 2 = 3k + 3

8k - 3k = 3 - 2

5k = 1

k = 1/5

Also, (-5k + (3/2))/(k + 1) = 5/12

-5k + (3/2) = 5/12(k + 1)

(-10k + 3)/2 = (5k + 5)/12

(-10k + 3) = (5k + 5)/6

6(-10k + 3) = 5k + 5

-60k + 18 = 5k + 5

18 - 5 = 5k + 60k

65k = 13

k = 13/65

k = 1/5

Therefore, the required ratio is 1:5

✦ Try This: Find the ratio in which point T (-1, 6) divides the line segment joining the points P (-3, 10) and Q (6, -8).

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

NCERT Exemplar Class 10 Maths Exercise 7.3 Problem 11

Find the ratio in which the point P(3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, –5)

Summary:

The ratio in which the point P(3/4, 5/12) divides the line segment joining the points A (1/2, 3/2) and B (2, –5) is 1:5

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