The line bisecting a given line segment 
can be constructed geometrically, as illustrated above.
Line Bisector
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References
Courant, R. and Robbins, H. "How to Bisect a Segment and Find the Center of a Circle with the Compass Alone." §3.4.4 in What Is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 145-146, 1996.Dixon, R. Mathographics. New York: Dover, p. 22, 1991.Referenced on Wolfram|Alpha
Line BisectorCite this as:
Weisstein, Eric W. "Line Bisector." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LineBisector.html