Question

The line segment joining A(−2, 9) and B(6, 3) is a diameter of a circle with centre C. Find the coordinates of C.

Answer 1

The given points are A(−2, 9) and B(6, 3).
Then, C(x, y) is the midpoint of AB.
$$\begin{gathered} x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2} \\ \Rightarrow x=\frac{-2+6}{2},y=\frac{9+3}{2} \\ \Rightarrow x=\frac{4}{2},y=\frac{12}{2} \\ \Rightarrow x=2,y=6 \end{gathered}$$
Therefore, the coordinates of point C are (2, 6).