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Question
One end of the diameter of a circle is (–2, 5). Find the co-ordinates of the other end of it, if the centre of the circle is (2, –1).
Solution
We know that the centre is the mid-point of diameter.
Let the required co-ordinates of the other end of mid-point be (x, y).
∴ `(2, -1) = ((-2 + x)/2, (5 + y)/2)`
`=> 2 = (-2 + x)/2` and `-1 = (5 + y)/2`
`=>` 4 = –2 + x and –2 = 5 + y
`=>` 6 = x and –7 = y
Thus, the required co-ordinates are (6, −7).
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