Question

f 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)      

•  (6, 7)      

• (−6,−7)       

Answer 1

Let O(−2, 5) be the centre of the given circle and A(2, 3) and B(x, y) be the end points of a diameter of the circle.

Then, O is the mid-point of AB.

Using mid-point formula, we have

\[\therefore \frac{2 + x}{2} = - 2\]  and  \[\frac{3 + y}{2} = 5\]

\[\Rightarrow 2 + x = - 4\]  and \[3 + y = 10\]

 

\[\Rightarrow x = - 6\]  and  \[y = 7\]

 

Thus, the coordinates of the other end of the diameter are (−6, 7).
Hence, the correct answer is option A.