If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (−2, 5),
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) $(4,2)$
(d) $(5,3)$
Solution:
Let (x, y) be the coordinates of the other end of the diameter. Then
$-2=\frac{2+x}{2} \Rightarrow x=-6$
$5=\frac{3+y}{2} \Rightarrow y=7$
Hence, the correct answer is option (a).