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)

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.

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

Let the given line 2x + y - 4 = 0 divide the line segment joining the points A(2, - 2) and B(3, 7) in a ratio k: 1 at point C.

Coordinates of the point of divison

C (x, y) = [(3k + 2) / (k + 1), (7k - 2) / (k + 1)]

Hence, x = (3k + 2) / (k + 1), y = (7k - 2) / (k + 1)

This point C also lies on 2x + y - 4 = 0 .....(1)

By substituting the values of C(x, y) in Equation(1),

2[(3k + 2) / (k + 1)] + [(7k - 2) / (k + 1)] - 4 = 0

[6k + 4 + 7k - 2 - 4k - 4] / (k + 1) = 0 (By Cross multiplying & Transposing)

9k - 2 = 0

k = 2/9

Therefore, the ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A (2, 2) and B (3, 7) is 2:9 internally.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 7

Video Solution:

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).

NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.4 Question 1

Summary:

The ratio in which the line 2x + y - 4 = 0 divides the line segment joining the points A (2, - 2) and B (3, 7) is 2 : 9.

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