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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]

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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

2+x2=-2 and 3+y2=5

2+x=-4 and 3+y=10

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.

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