Final answer:
The center of the circle is (-5, -7) and the radius is 5, found by determining the midpoint of the diameter's endpoints and calculating half of the diameter's length, respectively. Therefore, the answer is option (a).
Correct option is a) Center: (-5, -7), Radius: 5
Step-by-step explanation:
The question involves finding the center and radius of a circle given the endpoints of its diameter. The diameter has endpoints (-10, -7) and (0, -7). To find the center, we calculate the midpoint of the diameter's endpoints by averaging their x and y coordinates. Thus, the center is:
- x-coordinate: (-10 + 0) / 2 = -5
- y-coordinate: (-7 + -7) / 2 = -7
So, the center is at the point (-5, -7).
To find the radius, we calculate the distance between one of the endpoints of the diameter and the center. Since the y-coordinates are the same, the distance is simply the difference in the x-coordinates divided by 2:
- Radius: (0 - (-10)) / 2 = 10 / 2 = 5
Therefore, the radius of the circle is 5. The correct answer is option (a), which gives the center as (-5, -7) and the radius as 5.