Question

The coordinates of the ends of a diameter of a circle are \( (-10, 6) \) and \( (6, -10) \). Then the coordinates of its centre are:

• A. \( (-8, -8) \)
• B. \( (-8, 4) \)
• C. \( (-2, -2) \)
• D. \( (2, 4) \)

Hint:

For any chord (including the diameter), the midpoint of its endpoints gives the point on the circle’s perpendicular bisector; for a diameter, this midpoint is exactly the centre.

Answer 1

The Correct Option is C

Step 1: Use the midpoint formula for the centre.
For endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) of a diameter, the centre is
\[ \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right). \]
Step 2: Substitute the given points.
\[ \left(\frac{-10+6}{2}, \frac{6+(-10)}{2}\right) = \left(\frac{-4}{2}, \frac{-4}{2}\right) = (-2, -2). \]
Step 3: Conclude.
Therefore, the centre of the circle is \( (-2, -2) \).