6. $\left(15\right.$ points) Three material points with masses $m_{1}=2$ kg, $m_{2}=3$ kg, and $m_{3}=4$ kg are arranged sequentially on a straight line. The distance between points 1 and 2 is $25 \mathrm{~cm}$. The distance between points 2 and 3 is 75 cm. Determine the distance from point 1 to the center of mass of this system of three points.
Answer: 52.8 cm.

Solution. By the definition of the center of mass $x_{\text {center }}=\frac{m_{1} \cdot 0+m_{2} \cdot 25+m_{3} \cdot 100}{m_{1}+m_{2}+m_{3}}=52.8$ cm.