Question

The line segment 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). Since C is the centre and AB is the diameter, C is the midpoint of AB.

Let Coordinates of C be (x, y)

$x=\frac{(x1+x2)}{2}$

⇒ $x=\frac{(-2+6)}{2}$

⇒$x=\frac{4}{2}$

⇒ x = 2

$y=\frac{(y1+y2)}{2}$

⇒$y=\frac{(9+3)}{2}$

⇒ $y=\frac{(12}{2})$

⇒ y = 6

Therefore, the co-ordinates of point C are (2, 6)