Question

Question 7
Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, - 3) and B is (1, 4).

Answer 1

Let the coordinates of point A be (x, y).
Mid-point of AB is (2, - 3), which is the center of the circle.
$\therefore (2,-3)=(\frac{x+1}{2},\frac{y+4}{2})$
$\Rightarrow \frac{x+1}{2}=2$ and $\frac{y+4}{2}=-3$
$\Rightarrow x+1=4$ and $y+4=-6$
$\Rightarrow x=3$ and $y=-10$
Therefore, the coordinates of A are (3,-10)