Question

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

Answer 1

The centre of a circle is the mid-point of each of its diameters.

$$C = \left(\frac{-3 + 7}{2}, \frac{1 + (-5)}{2}\right)$$

$$= \left(\frac{4}{2}, \frac{-4}{2}\right)$$

$$= (2, -2)$$

Hence the centre is $$C(2, -2)$$.