Question

The centre ‘O’ of a circle has the coordinates (4, 5) and one point on the circumference is (8, 10). Find the coordinates of the other end of the diameter of the circle through this point.

Answer 1

Let (x, y) be the coordinates of the other end of the diameter of the circle.

Since, centre is the midpoint of the diameter of the circle.
So coordinates of midpoint of diameter
AB = `((8 + x)/2 , (10 + y)/2)`
But O(4, 5) is the centre hence
`(8 + x)/2` = 4
⇒ x = 8 - 8 = 0.
Also `(10 + y)/2` = 5
⇒ y = 10 - 10 = 0.
Hence (0, 0) be the coordinates of the other end.