Question

The coordinates of diameter AB of a circle are A(2, 7) and B(4, 5), then find the coordinates of the centre

Answer 1

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

A(x₁, y₁) = A(2, 7), B(x₂, y₂) = B(4, 5)

∴ x₁ = 2, y₁ = 7, x₂ = 4, y₂ = 5

C is the mid-point of seg AB.

∴ By midpoint formula,

C(x, y) = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

= `((2 + 4)/2, (7 + 5)/2)`

= `(6/2, 12/2)`

∴ C(x, y) = C(3, 6)

∴ The co-ordinates of the centre of the circle are (3, 6).