To the find the midpoint of a segment you add the x values, then divide by 2, then add the y values and divide by 2. . Therefore, you would do ((4+8)/2, (9+7)/2). So, you're answer is (12/2, 16/2), which equals (6, 8)
You have to know the coordinates of the center and the radius. refer to this website for more information: http://www.mathwarehouse.com/geometry/circle/equation-of-a-circle.php