Final answer:
The midpoint of the line segment with endpoints (-8 1/2, 3) and (6, -1 1/2) is (-1 1/4, 3/4).
Step-by-step explanation:
The midpoint of a line segment is the point that divides the line segment into two equal parts. It is found by calculating the averages of the x-coordinates and the y-coordinates of the endpoints. For the line segment with endpoints (-8 1/2, 3) and (6, -1 1/2), the midpoint can be found using the midpoint formula which is ((x1 + x2)/2, (y1 + y2)/2).
So for the x-coordinate of the midpoint:
((-8 1/2) + 6)/2 = (-17/2 + 12/2)/2 = (-5/2)/2 = -5/4 = -1 1/4
And for the y-coordinate of the midpoint:
(3 + (-1 1/2))/2 = (6/2 - 3/2)/2 = 3/2/2 = 3/4
Therefore, the midpoint of the line segment is (-1 1/4, 3/4).