Find the coordinates of the center of the circle if the ends of its diameter are points A (-4; 2) and B (6; -8).

The diameter of a circle is a line segment that connects two points on a circle and passes through its center. The diameter is halved by the center of the circle. Thus, first we need to find the coordinates of the midpoint of the segment, which are calculated by the formulas:
x = (x1 + x2) / 2;
y = (y1 + y2) / 2,
where x1 and y1 and x2 and y2 are the coordinates of the ends of the segment.
Find the coordinates of the midpoint of the segment AB of point C:
x = (- 4 + 6) / 2 = 2/2 = 1;
y = (2 + (- 8)) / 2 = (2 – 8) / 2 = – 6/2 = – 3.
Point C has coordinates (1; – 3).
Answer: C (1; – 3).