Question

The centre of a circle is at $(-6,4)$. If one end of a diameter of the circle is at the origin, then find the other end.

• A. $(-12,8)$
• B. $(-12,-8)$
• C. $(12,8)$
• D. None of these

Answer 1

The correct option is A $(-12,8)$

Take coordinate of other end of diameter as $P(x,y)$.

since, origin divides the diameter of a circle in $2$ equal parts, hence origin will be mid-point of $(0,0)$ and $(x,y)$.

By midpoint theorem:

$x=\frac{x_1+x_2}{2}$ and $y=\frac{y_1+y_2}{2}$

$⟹-6=\frac{0+x}{2}=\frac{x}{2}$

$⟹x=-12$

And,

$⟹4=\frac{y+0}{2}=\frac{y}{2}$

$⟹y=8$.

So, $P(x,y)=(-12,8)$