The world does not come with a coordinate system attached to it. A coordinate system is an artificially imposed grid that you place on a problem in order to make quantitative measurements. You are free to choose:

• Where to place the origin, and

• How to orient the axes.

Different problem solvers may choose to use different coordinate systems; that is perfectly acceptable. However, some coordinate systems will make a problem easier to solve. Part of our goal is to learn how to choose an appropriate coordinate system for each problem.

FIGURE 3.9 shows the xy-coordinate system we will use in this book. The placement of the axes is not entirely arbitrary: the positive y-axis is always located $90\text{°}$ counterclockwise (ccw) from the positive x-axis. Figure 3.9 also identifies the four quadrants of the coordinate system, I through IV.

FIGURE 3.9 A conventional $xy$-coordinate system and the quadrants of the $xy$-plane.

Coordinate axes have a positive end and a negative end, separated by zero at the origin where the two axes cross. When you draw a coordinate system, it is important to label the axes. This is done by placing x and y labels at the positive ends of the axes, as in Figure 3.9. The purpose of the labels is twofold:

• To identify which axis is which, and

• To identify the positive ends of the axes.

This will be important when you need to determine whether the quantities in a problem should be assigned positive or negative values. This textbook will follow the convention that the positive direction of the x-axis is to the right and the positive direction of the y-axis is up.