Question

The centre of a circle is $C(-3,6)$ and one end of a diameter is $A(4,-8)$, 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 $A(-3,6)$

Midpoint of $AB=(\frac{\alpha +4}{2},\frac{\beta -8}{2})$

Since the centre $C(-3,6)$ of the circle is the mid-point of $AB$,

$\frac{\alpha +4}{2}=-3$ and $\frac{\beta -8}{2}=6$

$\Rightarrow \alpha +4=-6$ and $\beta -8=12$

$\Rightarrow \alpha =-6-4=-10$ and $\beta =12+8=20$

$\therefore$The coordinates of the other end of the diameter are $(-10,20)$