# Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4)

**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.

Let the coordinates of point A be (x, y).

Mid-point of AB is C (2, - 3), which is the center of the circle.

Therefore, (2, -3) = ((x + 1) / 2, (y + 4) / 2)

⇒ (x + 1) / 2 = 2 and (y + 4) / 2 = - 3 (By Cross multiplying & transposing)

⇒ x + 1 = 4 and y + 4 = - 6

⇒ x = 3 and y = - 10

Therefore, the coordinates of A are (3, - 10)

**Video Solution:**

## Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4)

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

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4)

The coordinates of a point A, where AB is the diameter of a circle whose centre is (2, - 3) and B is (1, 4) is (3, -10)