Question

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (–2, 5) then the coordinates of the other end of the diameter are ______.

Options

• (–6, 7)

• (6, –7)

• (4, 2)

• (5, 3)

Answer 1

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (–2, 5) then the coordinates of the other end of the diameter are (–6, 7).

Explanation:

The centre is the midpoint of the diameter. If A(2, 3) and B(x, y) are endpoints and C(–2, 5) is the midpoint, then `(2 + x)/2 = -2` → x = –6 and `(3 + y)/2 = 5` → y = 7.

Hence, B = (–6, 7).