Question

The centre of a circle is $C(-1,2)$ and one end of a diameter is $A(6,7)$. 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 $A(6,7)$

Midpoint of $AB=(\frac{\alpha +6}{2},\frac{\beta +7}{2})$

Since the centre $C(-1,2)$ of the circle is the mid-point of $AB$,

$\frac{\alpha +6}{2}=-1$ and $\frac{\beta +7}{2}=2$

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

$\Rightarrow \alpha =-2-6=-8$ and $\beta =4-7=-3$

$\therefore$The coordinates of the other end of the diameter are

$(-8,-3)$