Let C(x, y) be the Centre of the Circle,
\(A\left(x_1, y_1\right)=A(-2,7), \quad B\left(x_2, y_2\right)=(4,5) \)
\(\therefore x_1=-2, \ y_1=7, \quad x_2=4, \ y_2=5\)
C is the mid-point of line segment AB.
\(\therefore\) By midpoint formula,
\(c(x, y) =\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right) \)
\(=\left(\frac{-2+4}{2}, \frac{7+5}{2}\right) \)
\(=\left(\frac{2}{2}, \frac{12}{2}\right) \)
= (1, 6)
\(\therefore C(x, y) =C(1,6)\)
\(\therefore\) The co-ordinates of the centre of the circle are (1, 6).
