if AB is the diameter of a circle with Centre O (1,-3) and the coordinates of A are (4 ,-1) find the the coordinates of B .
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if AB is the diameter of a circle with Centre O (1,-3) and the coordinates of A are (4 ,-1)
if AB is the diameter of a circle with Centre O (1,-3) and the coordinates of A are (4 ,-1) find the the coordinates of B .
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Step-by-step explanation:
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
(x+4 /2 , y-1 /2)
But, the coordinates of C are given to be (1,-3).
∴
x+4 / 2 =1 and y-1 / 2 =-3
⇒x+4=2 and y−1=−6
⇒x=−2 and y=−5
Hence,the coordinates of B are (-2, -5).