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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:
Options
A. (−6, 7)
B. (6, −7)
C. (6, 7)
D. (−6, −7)
Solution
Let AB be the diameter and O be the centre of the circle.
We are given co-ordinates of one end point of circle and co-ordinates of its centre.
So, co-ordinates of A are (2, 3) and centre O are (−2, 5).
Let co-ordinates of point B be (x, y).
We know that centre of a circle is the midpoint of the diameter.
∴ By midpoint formula,
`-2=(2+x)/2` and `5=(3+y)/2`
`rArr=-4=2+`and`10=3+y`
`rArrx=-6`and`y=7`
So, other end of the diameter is (−6, 7).
Hence, the correct answer is A.
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