Splitting
Squares

     On the coordinate plane a "unit square" is drawn with the following vertices: P(1, 0), Q(2, 0), R(2, 1) and S(1, 1). See drawing.

     A line is drawn from the origin that cuts the square into two sections, one larger than the other. The ratio of the areas of the upper section to the lower is 2:1.

     Determine the equation of the "cutting" line.


Extensions to the problem:


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