Question

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).

Answer 1

Given: A circle with centre ‘C’ (2, -3). \(\overline{AB}\) is a diameter where 

B = (1, 4); A = (x, y). 

C is the midpoint of AB. 

[∵ Centre of a circle is the midpoint of the diameter]

4 = x + 1 and – 6 = y + 4 

⇒ x = 4 – 1 = 3 and y = -6 – 4 = -10 

A (x, y) = (3, -10)