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

Answer 1

Since centre is the mid point of the end points of the diameter
Let the other end of diameter is $(x,y)$

$(-6,4)=(\frac{x+0}{2},\frac{y+0}{2})$

$-6=\frac{x+0}{2}$ And $4=\frac{y+0}{2}$

$-6\times 2=x$ and $4\times 2=y$
$-12=x$ and $8=y$
$x=-12$ and $y=8$
Hence required answer= $(-12,8)$