Final answer:
The center of the circle with endpoints (-5, -6) and (4, 2) is located at (-0.5, -2), which is found by calculating the midpoint of the line segment connecting the two points. correct option is B.
Step-by-step explanation:
The student has asked for the center of the circle that has endpoints at (-5, -6) and (4, 2). To determine the center of a circle given any two endpoints of a diameter, one should find the midpoint of the line segment that connects these two points.
The midpoint M can be found using the midpoint formula, which is M = ((x1 + x2)/2, (y1 + y2)/2). Applying this formula to our points (-5, -6) and (4, 2), we get M = ((-5 + 4)/2, (-6 + 2)/2) = (-1/2, -4/2) = (-0.5, -2).
Therefore, the center of the circle is located at (-0.5, -2), which is the midpoint between the two given endpoints. This is the point from which all points on the circumference of the circle are equidistant which is found by calculating the midpoint of the line segment connecting the two points..