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).