Question

The centre of a circle with (1, 2) and (7, -4), as end points of the diameter is

• A. (-4, 1)
• B. (4, -1)
• C. (-4, -1)
• D. (4, 1)

Answer 1

The Correct Option is B

To solve the problem, we need to find the centre of a circle when the endpoints of its diameter are given as (1, 2) and (7, –4).

1. Understanding the Concept:
The centre of a circle is the midpoint of the diameter. If the endpoints of the diameter are \( (x_1, y_1) \) and \( (x_2, y_2) \), then the midpoint is given by:

\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

2. Substitute the values:
Given points: \( (1, 2) \) and \( (7, -4) \)

\[ x = \frac{1 + 7}{2} = \frac{8}{2} = 4 \]
\[ y = \frac{2 + (-4)}{2} = \frac{-2}{2} = -1 \]

3. Calculate the Coordinates of the Centre:
The centre of the circle is at \( (4, -1) \).

Final Answer:
The correct answer is option (B): (4, –1).