Question

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 .​

Answer 1

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).