A halving line of an even-sized finite set 
of points
in the plane, with no three collinear,
is a line through two members that has 
other members in each open half-plane.
For the four vertices of a square,
the two diagonals are the halving lines of this
point set.
Halving Line
See also
Collinear, Half-Plane, LineExplore with Wolfram|Alpha
References
Dey, T. K. "Improved Bounds for Planar
-Sets and Related Problems." Disc. Comput. Geom. 19,
373-382, 1998. https://doi.org/10.1007/PL00009354.
Cite this as:
Weisstein, Eric W. "Halving Line." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HalvingLine.html