Before creating the design, the weaver marks two places on the rug (usually using chalk):
1) By counting the weft strands and dividing by two, she finds the horizontal center of the rug.
This is the equivalent of finding X = 0.
2) Using a loose strand of yarn, she determines the total height that the rug will be. She then folds the yarn in half, and uses this measure to mark the vertical center of the rug.
This is the equivalent of finding Y = 0.
Therefore, for the rug on the right, the center of the rug is defined where X = 0 (determined by weft count) and Y = 0 (determined by yarn length), which is the Origin on a cartesian grid.
While weaving, the weaver will often count the number of wefts in each design element to ensure that the rug to the right of the horizontal center is an exact reflection of the rug's left side. At the vertical center, the weaver often reflects the design across the X axis. This process of counting to keep track of where design elements are to be placed is crucial for making the rugs symmetrical in appearance. 
