Question

If A(1, 1) and B(7, 9) are the end points of a diameter of a circle, then find the coordinates of the centre of the circle.

Answer 1

Given two points A(1, 1) and B(7, 9) are the end points of a diameter of a circle.

Since, the centre of the circle divides the diameter into two equal parts and it is the mid-point of the two end points of the diameter.

Let the centre of the circle be C(x, y).

So, mid-point C(x, y) = `((a_1 + a_2)/(2), (b_1 + b_2)/(2))`

Here, (a₁, b₁) = (1, 1) and (a₂, b₂) = (7, 9)

∴ (x. y) = `((1 + 7)/(2), (1 + 9)/(2))`

= `(8/2, 10/2)`

= (4, 5)

Therefore, the coordinates of the centre of the circle is ( 4, 5).