Why can not a line segment have more than one midpoint
Because the definition of a line segment is a segment with two endpoints. If there are only two endpoints then there can only be one middle, hence one midpoint.
To understand why a line segment cannot have more than one midpoint, let's first define what a midpoint is.
A midpoint is a point that divides a line segment into two equal parts. In other words, it is the point that is equidistant from both endpoints of the line segment.
Now, consider a line segment with two distinct midpoints, let's call them M1 and M2.
If M1 is truly a midpoint, it means that it is equidistant from both endpoints. Similarly, if M2 is also a midpoint, it should also be equidistant from the same two endpoints.
However, if M1 and M2 are both midpoints, this would mean that M1 and M2 are equidistant from each endpoint.
This creates a contradiction because, by definition, the two endpoints are the only points on the line segment that are equidistant from each endpoint.
Therefore, it is not possible for a line segment to have more than one midpoint.