6. (15 points) Three material points with masses $m_{1}=100$ g, $m_{2}=200$ g, and $m_{3}=400$ g are arranged sequentially on a straight line. The distance between points 1 and 2 is 50 cm. The distance between points 2 and 3 is 200 cm. Determine the distance from point 1 to the center of mass of this system of three points.