Question

One end of the diameter of a circle is $(6,9)$ and the centre is $(0,0)$. Find the co-ordinate of the other end of the diameter.

Answer 1

Coordinate of one end of diameter of circle $=(6,9)$

Centre of circle $=(0,0)$

Let $(h,k)$ be the other end of the diameter of crcle.

As we know that centre of circle is the mid-point of diameter of circle.

Therefore,

$(\frac{h+6}{2},\frac{k+9}{2})=0$

$\Rightarrow \frac{h+6}{2}=0\Rightarrow h=-6$

$\Rightarrow \frac{k+9}{2}=0\Rightarrow k=-9$

Hence the other end of diameter of circle is $(-6,-9)$.