Question

One end of diameter of circle is $(3,2)$ and center of circle is origin then find the other end of diameter.

Answer 1

One end of the diameter of the circle $=(3,2)$

Center of the circle $=(0,0)$

Let, the other end of the diameter of the circle $=(x,y)$

Since the center is the mid-point of the diameter of the circle,

$(0,0)=(\frac{3+x}{2},\frac{2+y}{2})$

$\Rightarrow \frac{3+x}{2}=0$ and $\frac{2+y}{2}=0$

$\Rightarrow 3+x=0$ and $2+y=0$

$\Rightarrow x=-3$ and $y=-2$

Hence, the other end of the diameter of the circle is $(-3,-2).$