# Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, – 3) and B is (1,4).

Let the coordinates of point A be (x, y).

Mid-point of AB is (2, – 3), which is the centre of the circle.

Coordinate of B = (1, 4)
(2, -3) =$$(\frac{x+1}{2} , \frac{y+4}{2} )$$
$$\frac{x+1}{2} = 2$$
$$\Rightarrow x+1= 4$$
$$\Rightarrow x = 4-1 = 3$$
and$$\frac{y+4}{2} = -3$$
$$\Rightarrow y+4 = -6$$
$$\Rightarrow y = -6-4 = -10$$
$$\therefore$$ x = 3 and y = -10
The coordinates of A(3,-10).