# Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts

**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.

By observation, that points P, Q, R divides the line segment A (- 2, 2) and B (2, 8) into four equal parts.

Point P divides the line segment AQ into two equal parts.

Therefore, AP : PB is 1 : 3

Using section formula which is given by P (x, y) = [mx_{2} + nx_{1 }/ m + n , my_{2} + ny_{1 }/ m + n]

Hence, coordinates of P = ((1 × 2 + 3 × (- 2)) / (3 + 1), (1 × 8 + 3 × 2) / (3 + 1)) = (- 1, 7 / 2)

Point Q divides the line segment AB into two equal parts

Q = ((2 + (- 2)) / 2, (2 + 8) / 2) = (0, 5)

Point R divides the line segment BQ into two equal parts

Coordinates of R = ((3 × 2 + 1 × (- 2)) / (3 + 1)] , [(3 × 8 + 1 × 2) / (3 + 1)) = (1,13/2)

**Video Solution:**

## Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts

### NCERT Class 10 Maths Solutions - Chapter 7 Exercise 7.2 Question 9:

Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts

The coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts is (- 1, 7 / 2), (0, 5) and (1, 13/2)