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

• A. (−6, 7)

• B. (6, −7)

• C. (6, 7)

• D. (−6, −7)

Answer 1

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.

∴ By midpoint formula,

`-2=(2+x)/2` and `5=(3+y)/2`

`rArr=-4=2+`and`10=3+y`

`rArrx=-6`and`y=7`

So, other end of the diameter is (−6, 7).

Hence, the correct answer is A.