a point at or near the middle of, or equidistant from, both ends, as of a line: the midpoint of a boundary.
a point in time halfway between the beginning and the end, as of a process, event, or situation: the midpoint of the negotiations.
Geometry. the point on a line segment or an arc that is equidistant, when measured along the line or the arc, from both endpoints.
Statistics. median ( def 5 ).
Astrology. the point on the arc that is equidistant from two planets: regarded as a sensitive point and used in horoscopic interpretations.
Also, mid-point.

1325–75; Middle English. See mid-, point

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World English Dictionary
midpoint (ˈmɪdˌpɔɪnt)
1.  the point on a line that is at an equal distance from either end
2.  a point in time halfway between the beginning and end of an event

Collins English Dictionary - Complete & Unabridged 10th Edition
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Example sentences
Use a protractor to draw the angled tops and the mitered midpoint of the folded
  and half-and-half roofs.
It helped them stay at the midpoint between the two brains.
If an instructor reports a student as withdrawn by the midpoint of the term,
  the student won't get the second half of the grant.
But it seems to me that the midpoint of the semester is a good time for
  self-evaluation as well.
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