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).

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)