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 .

`x = (x_1+x_2)/2, y = (y_1 +y_2) /2`

`⇒ x = (-2+6)/2, y = (9+3)/2`

`⇒ x = 4/2, y = 12/2 `

`⇒ x = 2, y=6`

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