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 :

• A. (-6,7)
• B. (6,-7)
• C. (6,7)
• D. (-6,-7)

Answer 1

The correct option is A (-6,7)

Let AB be the diameter and O be the centre of the circle.

We are given co-ordinates of one end point of circle and co-ordinates of its centre.

So, co-ordinates of A are (2, 3) and centre O are (-2, 5).

Let co-ordinates of point B be (x, y).

We know that centre of a circle is the midpoint of the diameter.

$\therefore$ By midpoint formula,
$-2=\frac{2+x}{2}$ and $5=\frac{3+y}{2}$
$\Rightarrow -4=2+x$ and 10 =3+y
$\Rightarrow x=-6$ and y =7