The line segment joining A(-3, 1) and B(7, -5) is a diameter of a circle whose centre is C. Find the co-ordinates of the centre C.

Since the line segment joining points A and B is the diameter of the circle, the centre of the circle must be the mid-point of the diameter AB.

By using mid-point formula,

(x, y) = $\Big(\dfrac{x$1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

Substituting values we get :

$\Rightarrow C(x, y) = \Big(\dfrac{-3 + 7}{2}, \dfrac{1 + (-5)}{2}\Big) \\[1em] \Rightarrow C(x, y) = \Big(\dfrac{4}{2}, \dfrac{-4}{2}\Big) \\[1em] \Rightarrow C(x, y) = (2, -2).$

Hence, the coordinates of centre (C) are (2, -2).