Question

The co-ordinates of one end-point of a circle are (–3, 1) and the co-ordinates of the centre of the circle are (2, –4). The co-ordinates of the other end-point of the diameter are 

(a) \(\big(\frac{-1}{2},\frac{-3}{2}\big)\)

(b) (–7, 9) 

(c) (7, –9) 

(d) \(\big(\frac{1}{2},\frac{3}{2}\big)\)

Answer 1

(c) (7 , -9)

Let the co-ordinates of the other end point of the diameter be (x, y).

Then, \(\frac{-3+x}{2} = 2 \) and \(\frac{1+y}{2}=-4\)

⇒ – 3 + x = 4 and 1 + y = –8 

⇒ x = 7 and y = – 9