Introduction:
The center of mass is a point that represents the average position of the mass in a system. It is the point at which the entire mass of the system can be considered to be concentrated. In this case, we have three rods of the same mass placed in a specific arrangement. We need to determine the coordinates of the center of mass for this system.

Given Information:
- The rods are of equal mass.
- The rods are placed as shown in the figure.

Approach:
To find the center of mass of the system, we need to consider the mass and position of each rod. We can calculate the coordinates of the center of mass using the weighted average of the individual masses and their respective positions.

Calculating the Center of Mass:
We can break down the problem into two dimensions (x and y) and calculate the coordinates of the center of mass separately for each dimension.

For the x-coordinate:
To find the x-coordinate of the center of mass, we need to calculate the weighted average of the x-coordinates of the rods.
Let's assume the length of each rod is L.
- The left rod is at position (0, 0) with a mass of m.
- The middle rod is at position (L/2, 0) with a mass of m.
- The right rod is at position (L, 0) with a mass of m.

To find the x-coordinate of the center of mass (x_cm), we can use the formula:
x_cm = (m*x_1 + m*x_2 + m*x_3) / (m + m + m)

Simplifying the equation, we get:
x_cm = (0 + (L/2)*m + L*m) / (3m)
x_cm = (L/2 + L) / 3
x_cm = (3L/2) / 3
x_cm = L/2

Therefore, the x-coordinate of the center of mass is L/2.

For the y-coordinate:
Since all the rods are placed along the x-axis, the y-coordinate of the center of mass will be zero.

Conclusion:
The coordinates of the center of mass for the given system are (L/2, 0). The x-coordinate is L/2, and the y-coordinate is zero.