Question:
Find the coordinates of a point A, where AB is a diameter of the circle whose centre is (2, −3) and B is (1, 4).
Solution:
Let the co-ordinates of point A be $(x, y)$.
Centre lies on the mid-point of the diameter. So applying the mid-point formula we get,
$\frac{x+1}{2}=2$
$x=3$
Similarly,
$\frac{y+4}{2}=-3$
$y=-10$
So the co-ordinates of A are (3,−10)
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