# Find the coordinates of a point A,

Question.

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

Solution:

Here, centre of the circle is O(2, –3)

Let the end points of the diameter be A(x, y) and B(1, 4)

The centre of a circle bisects the diameter.

$\therefore \quad 2=\frac{\mathbf{x}+\mathbf{1}}{\mathbf{2}} \Rightarrow \mathbf{x}+1=4$ or $\mathbf{x}=3$

And $-3=\frac{\mathbf{y}+\mathbf{4}}{\mathbf{2}} \Rightarrow \mathrm{y}+4=-6$ or $\mathrm{y}=-10$

Here, the coordinates of $A$ are $(3,-10)$