Question

If the coordinates of the one end of a diameter of a circle are $(2,3)$ and the coordinates of its centre are $(-2,5),$ then the coordinates of the other end of the diameter are:

• A. $(-6,7)$
• B. $(6,-7)$
• C. $(6,7)$
• D. $(-6,-7)$

Answer 1

The correct option is A $(-6,7)$

Let the coordinates of the one end of a diameter $AB$ of a circle are $A(2,3)$ and $B(x,y).$

Let the coordinates of the center of the circle $C(-2,5).$

As center is the midpoint of the diameter $AB$ so the coordinates of center is

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

Now equating the coordinates of center we get

$\frac{2+x}{2}=-2$

$\Rightarrow 2+x=-4$

$\Rightarrow x=-4-2$

$\Rightarrow x=-6$

$\frac{3+y}{2}=5$

$\Rightarrow 3+y=10$

$\Rightarrow y=10-3$

$\Rightarrow y=7$

$\therefore$Coordinates of $B=(-6,7).$