# Find the coordinates of a point A,

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)