Question

The coordinates of one end point of a diameter AB of a circle are A(4, −1) and the coordinates of the centre of the circle are C(1, −3). Then, the coordinates of B are


(a) (2, −5)
(b) (−2, 5)
(c) (−2, −5)
(d) (2, 5)

Answer 1

(c) (−2, −5)
Let the coordinates of B be (a, b). Then,
$\text{Midpoint of}AB=\left(\frac{4+a}{2},\frac{-1+b}{2}\right)$
But the midpoint C(1, −3) is given.
Therefore,
$$\begin{gathered} \frac{4+a}{2}=1\text{and}\frac{-1+b}{2}=-3 \\ \Rightarrow 4+a=2\text{and}-1+b=-6 \\ \Rightarrow a=-2\text{and}b=-5. \end{gathered}$$
Hence, the coordinates of B are (−2, −5).