(Dis)prove: Given a plane of arbitrary size and n dots that can be placed on this plane, a line of symmetry can be defined such that on each side of the line an equal number of dots rest (including colinear points). This line doesn't necessarily need to divide the plane into two, it just needs to have an equal number of dots on either side. Can it be (dis)proven that such a line that passes through at least one dot exists for every n.