Final answer:
The center of the circle determined from the given points (-6, -1) and (6, 1) is (0, 0). These points are the endpoints of the diameter itself, so the given points are already the correct endpoints of the diameter.
"the correct option is approximately option B"
Step-by-step explanation:
To determine the endpoints of a diameter given two points that lie on a circle, we must first understand that a diameter of a circle is a straight line that passes through the center of the circle and whose endpoints are on the circle. The two points given, (-6, -1) and (6, 1), are endpoints of a diameter, so the center of the circle is the midpoint between these two points.
Let's find the midpoint, which is the center of the circle, using the midpoint formula (which is the average of the x-coordinates and the average of the y-coordinates):
- Middle point (x) = (x1 + x2) / 2 = (-6 + 6) / 2 = 0
- Middle point (y) = (y1 + y2) / 2 = (-1 + 1) / 2 = 0
So the center of the circle is at (0, 0). Since the points (-6, -1) and (6, 1) are already at opposite ends of a diameter, and we have confirmed that (0, 0) is the center, these points are correct as-is and do not need to be altered to find the endpoints of the diameter.