# 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(x₁, y₁) and B(x₂, y₂), internally, in the ratio m₁_{ }: m₂ is given by the section formula.

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

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

According to the mid point formula,

O(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

We have A(x, y) and B(1, 4) and the center is (2, -3)

Therefore by using midpoint formula,

(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)

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

**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

**Summary:**

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).

**☛ Related Questions:**

- If A and B are (- 2, - 2) and (2, - 4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.
- Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.
- Find the area of a rhombus if its vertices are (3, 0), (4, 5), (- 1, 4) and (- 2, - 1) taken in order. [Hint: Area of a rhombus =1/2 x (product of its diagonals)]
- Find the ratio in which the line segment joining the points (- 3, 10) and (6, - 8) is divided by (- 1, 6).

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