# 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(x_{1}, y_{1}) and B(x_{2}, y_{2}), internally, in the ratio m_{1}: m_{2} is given by the Section Formula.

P (x, y) = [(mx_{2} + nx_{1}) / (m + n) , (my_{2} + ny_{1}) / (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)]

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

**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:

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)

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