If the coordinates of the end points of a circle are A(1,2) B(5,6) then find the coordinate of the center of the circle
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Let AB be a diameter of the circle having its centre at C(1, -3) such that the coordinates of one end A are (4, -1).
Let the coordinates of B be (x,y).
Since C is the mid-point of AB. Therefore,the coordinates of C are(
2
x+4
,
2
y−1
).
But, the coordinates of C are given to be (1,-3).
∴
2
x+4
=1and
2
y−1
=−3
⇒x+4=2andy−1=−6
⇒x=−2andy=−5
Hence,the coordinates of B are (-2, -5).
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