Final answer:
The center of the circle is at (0, 0), the diameter is approximately 12.17 units, and the radius is approximately 6.08 units.
Step-by-step explanation:
The question asks for information related to the endpoints of a diameter of a circle. Given endpoints at (-6, -1) and (6, 1), we can find the center, length of the diameter, and radius of the circle using these coordinates.
Steps to Determine the Circle's Information:
- Calculate the midpoint of the endpoints, which represents the center of the circle (h, k).
- Use the distance formula to find the length of the diameter D.
- Divide the diameter by 2 to find the radius r.
To find the center (h, k), add the x-coordinates and y-coordinates of the endpoints separately and divide each sum by 2:
Center (h, k) = ((-6 + 6)/2, (-1 + 1)/2) = (0, 0)
Now, using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we calculate D:
D = √((6 - (-6))² + (1 - (-1))²) = √(144 + 4) = √148 ≈ 12.17 units
The radius r is half the diameter, so r = D/2 ≈ 12.17/2 ≈ 6.08 units.
Summary:
The center of the circle is at (0, 0), the diameter is approximately 12.17 units, and the radius is approximately 6.08 units.