The coordinates of one end point of a diameter of a circle are (5, 2). If the coordinates of its centre are (2, 3), then the coordinates of the other end of diameter are ______.

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The coordinates of one end point of a diameter of a circle are (5, 2). If the coordinates of its centre are (2, 3), then the coordinates of the other end of diameter are (−1, 4). Explanation: Let the other end be (x, y), The centre (2, 3) is the midpoint of (5, 2) and (x, y), So, by the midpoint formula: = ((5 + x)/2, (2 + y)/2) = (2, 3) Equating coordinates gives: ⇒ 5 + x = 4 x = −1 ⇒ 2 + y = 6 y = 4 Hence, the other end is (−1, 4).

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