Does a line always have a midpoint?
False! A line, by definition, continues off to infinity in both directions. Therefore, it doesn’t have a midpoint. If you think of the number line, you might consider 0 to be its midpoint. However, that’s not quite accurate. You could just as easily consider 347 to be the midpoint, since for any integer n, you can find (347 + n) and (347 – n) on the number line. By this reasoning, 347 is just as good of a “midpoint candidate” as 0 is. A line segment will always have a midpoint, but a line segment isn’t the same thing as a line. Hope that helps!
