Question

The coordinates of one end point of a diameter of a circle are (4, -1) and the coordinates of the centre of the circle are (1, -3). Find the coordinates of the other end of the diameter.

Answer 1

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$(\frac{x+4}{2},\frac{y-1}{2})$.

But, the coordinates of C are given to be (1,-3).

$\therefore \frac{x+4}{2}=1and\frac{y-1}{2}=-3$

$\Rightarrow x+4=2andy-1=-6$

$\Rightarrow x=-2andy=-5$
Hence,the coordinates of B are (-2, -5).