Question

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

Options

• (−1, −4)

• (1, −4)

• (−1, 4)

• (1, 4)

Answer 1

The coordinates of one end point of a diameter of a circle are (5, 2). If the coordinates of its centre are (2, 3), then the coordinates of the other end of diameter are (−1, 4).

Explanation:

Let the other end be (x, y),

The centre (2, 3) is the midpoint of (5, 2) and (x, y),

So, by the midpoint formula:

= `((5 + x)/2, (2 + y)/2)`

= (2, 3)

Equating coordinates gives:

⇒ 5 + x = 4

x = −1

⇒ 2 + y = 6

y = 4

Hence, the other end is (−1, 4).