Question

AB is a diameter of a circle, where the

coordinates of centre C are (1, - 3).

Find the coordinates of B, if

coordinates of A are (4, 1)​

Answer 1

Answer:

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Step-by-step explanation:

Let AB be the diameter of the circle center "C"

Let A (4, -1), B (x, y) and C (1, -3)

"C" is the midpoint of AB

⟹4+x2=1⟹x=−2

⟹1−y2=−3⟹y=−5

HenceB=(−2,−5)

Answer 2

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(

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).