Question

The co-ordinates of the ends of a diameter of a circle are (10, -6) and (-6, 10). Then the co-ordinates of the centre of the circle are

• A. (-2, -2)
• B. (2, 2)
• C. (-2, 2)
• D. (2, -2)

Hint:

This is a direct application of the midpoint formula. Remember that the center of a circle is always the midpoint of its diameter.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The center of a circle is the midpoint of any of its diameters. Therefore, we can find the center by calculating the midpoint of the given endpoints of the diameter.

Step 2: Key Formula or Approach:
The midpoint formula for endpoints \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ \text{Center} = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]

Step 3: Detailed Explanation:
The given endpoints of the diameter are \((10, -6)\) and \((-6, 10)\).
Let \((x_1, y_1) = (10, -6)\) and \((x_2, y_2) = (-6, 10)\).
Calculate the x-coordinate of the center:
\[ x_c = \frac{10 + (-6)}{2} = \frac{4}{2} = 2 \] Calculate the y-coordinate of the center:
\[ y_c = \frac{-6 + 10}{2} = \frac{4}{2} = 2 \] The coordinates of the center are \((2, 2)\).

Step 4: Final Answer:
The co-ordinates of the centre of the circle are (2, 2).