Final answer:
The center of mass and geometric center of the system of coins are both at the origin (0, 0).
Step-by-step explanation:
The center of mass and geometric center of a system can be different depending on the distribution of masses. In this case, the four coins are placed at the coordinates (3, 0), (0, 3), (-3, 0), and (0, -3). To compare the center of mass and geometric center, we need to calculate their positions.
To find the center of mass, we multiply the coordinates of each mass by their respective masses and sum them, then divide by the total mass. In this case, the masses are all the same, so we can ignore them. The center of mass coordinates are (0, 0), which is the origin.
The geometric center is simply the average of the coordinates of the masses. So we add the x and y coordinates of all the masses and divide by the total number of masses. In this case, the geometric center coordinates are also (0, 0), which is the same as the center of mass.