Cartesian Coordinates
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2-D Cartesian Coordinates
3-D Cartesian Coordinates

2-D Cartesian Coordinates

In Cartesian coordinate system, one deals with a group of mutually perpendicular axes (or planes). Figure 1 shows the 2-D Cartesian coordinate system that involves 2 axes (or a plane). The X and Y axes shown in the figure are perpendicular to each other.

    Figure 1

Position P shown in Figure 1 can be described as (x, y). In other words, starting from the origin, one can reach P by moving in the direction of the X axis by x and then in the direction of the Y axis by y. x & y are the 2-D Cartesian coordinates. A rectangle was drawn for this purpose. For this reason, the Cartesian coordinate system is also called the rectangular coordinate system. Sequence of the movements is not important here.

x & y shown in Figure 1 are called the components of the position and they are mutually independent. That is, a motion in the direction of the X axis is independent from a motion in the direction of the Y axis.

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3-D Cartesian Coordinates

The 3-D Cartesian coordinate system deals with 3 mutually perpendicular straight lines or axes (Figure 2). Again, one can describe the position of point P in terms of three Cartesian coordinates: x, y & z. Starting from the origin, one can reach point P by moving in the direction of the X axis by x, in the direction of the Y axis by y, and in the direction of the Z axis by z. The sequence here, again, does not matter.

    Figure 2

Note in Figure 2 that the Z axis is aligned vertically. This is the traditional 3-D Cartesian coordinate system and will be used consistently throughout this website. Those who are accustomed to the ISB convention, in which the Y axis is aligned vertically, should switch the axes properly.

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Young-Hoo Kwon, 1998-