Question

The centre of a circle is $C(3,5)$ and one end of a diameter is $A(4,3)$, find the coordinates of the other end.

Answer 1

Let the other end of the diameter of the given circle be $B(\alpha ,\beta )$ whose one end is $A(4,3)$

Midpoint of $AB=(\frac{\alpha +4}{2},\frac{\beta +3}{2})$

Since the centre $C(5,3)$ of the circle is the mid-point of $AB$,

$\frac{\alpha +4}{2}=3$ and $\frac{\beta +3}{2}=5$

$\Rightarrow \alpha +4=6$ and $\beta +3=10$

$\Rightarrow \alpha =6-4=2$ and $\beta =10-3=7$

$\therefore$The coordinates of the other end of the diameter are $(2,7)$