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A 100-gon P1 is drawn in the Cartesian plane. The sum of the x-coordinates of the 100 vertices equals 2009. The midpoints of the sides of P1 form a second 100-gon, P2. Finally, the midpoints of the sides of P2 form a third 100-gon, P3. Find the sum of the x-coordinates of the vertices of P3. 

 Mar 25, 2018

after two shifts, the vertices go back to the original. the 3rd 100-gon has the same vertices as the first. the sum is 2009. sorry I am bad at explaining, but I know for sure the answer is 2009

 Jul 26, 2018

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