Question

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)​

Answer 1

(refer to the attachment)

Given :

• AB is the diameter with O(2, -3) as centre.
• Coordinates of B(1, 4).

To Find :

• Coordinates of A.

Solution :

Here we are given the centre coordinates of a circle which has a diameter AB.

Here we have to use the Mid-Point formula to find the other coordinate of the diameter as the centre is given.

Required Formula :

• For x = (x₁ + x₂)/2

• For y = (y₁ + y₂)/2

Explanation :

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

• A(x, y)
• B(1, 4)
• O(2, -3)

So, first we have to find the value of x.

To find the value of x,

ATQ,

⇒ x = (x₁ + x₂)/2

where,

• x = 2
• x₂ = 1
• x₁ = x

Substituting the values,

⇒ 2 = (x + 1)/2

⇒ 2 × 2 = x + 1

⇒ 4 = x + 1

⇒ 4 - 1 = x

⇒ 3 = x

∴ x = 3.

Now, the value of y.

To find the value of y,

ATQ,

⇒ y = (y₁ + y₂)/2

where,

• y = -3
• y₂ = 4
• y₁ = y

Substituting the values,

⇒ -3 = (y + 4)/2

⇒ -3 × 2 = y + 4

⇒ -6 = y + 4

⇒ -6 - 4 = y

⇒ -10 = y

∴ y = -10.

Hence,

Coordinates of A(x, y) = A(3, -10).

Coordinates of A is (3, -10).