7.5 There are 100 points distributed on a straight line. We mark the midpoints of all possible line segments with these points as endpoints. How many such midpoints can we get at least?

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[Solution] Consider the 99 segments formed by the 1st point from the left and the 2nd, 3rd, ..., 100th points from the left, and the 99 midpoints of these segments. Clearly, these midpoints are all distinct. Similarly, considering from the right, we can also obtain 99 distinct midpoints. Clearly, there is exactly 1 midpoint that is repeated in these two sets of midpoints, which is the midpoint of the segment formed by the 1st point from the left and the 1st point from the right. Therefore, there are at least 197 midpoints.

On the other hand, when the distances between every two adjacent points among these 100 points are all equal, the midpoint of any segment with these points as endpoints is either one of these 100 points or the midpoint of a small segment between two adjacent points. Therefore, there are at most 197 such midpoints. In summary, the minimum number of midpoints of such segments is 197.