Question:
If the coordinates of 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) $(-6,-7)$ [CBSE 2012]
Solution:
Let O(−2, 5) be the centre of the given circle and A(2, 3) and B(x, y) be the end points of a diameter of the circle.
Then, O is the mid-point of AB.
Using mid-point formula, we have
$\therefore \frac{2+x}{2}=-2$ and $\frac{3+y}{2}=5$
$\Rightarrow 2+x=-4$ and $3+y=10$
$\Rightarrow x=-6$ and $y=7$
Thus, the coordinates of the other end of the diameter are (−6, 7).
Hence, the correct answer is option A.