The mid-point
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on the perpendicular bisector of the segment.
I line that intersects a segment at its midpoint.
The term bisector means that bi is the two of something (a cycle with two wheels is a bicycle, for instance). Therefore a bisector will split a segment, area, angle, into two equal parts.
on the perpendicular bisector of the segment.
Equidistant from the endpoints of the segment.