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

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.

Solution:

The given points are A(−2, 9) and B(6, 3).
Then, C(xy) is the midpoint of AB.

$x=\frac{x_{1}+x_{2}}{2}, y=\frac{y_{1}+y_{2}}{2}$

$\Rightarrow x=\frac{-2+6}{2}, y=\frac{9+3}{2}$

$\Rightarrow x=\frac{4}{2}, y=\frac{12}{2}$

$\Rightarrow x=2, y=6$

Therefore, the coordinates of point C are (2, 6).