Two-dimensional rectangular coordinate system is usually set by two mutually perpendicular coordinate axes, which are usually called X axis and Y axis respectively. The intersection of two coordinate axes, called the Origin, is usually marked with O, which means "zero" and is also the first letter of the English word "origin". Each axis points in a specific direction. The coordinate axes of these two different lines define a plane, which is called xy plane, also called Cartesian plane. Usually, as long as the two axes are perpendicular to each other, it doesn't matter where to analyze the problem, but habitually (see the right picture), the X axis is placed horizontally, called the horizontal axis, which usually points to the right; The y axis is placed vertically, called the longitudinal axis, and usually points upward. This positional relationship between the two coordinate axes is called two-dimensional right-handed coordinate system, or right-handed coordinate system. If you draw this right hand tie on a piece of transparent paper, no matter how you rotate in the plane, what you get is called right hand tie; But if you turn the paper over, the coordinate system you see on the back is called "left-handed system". This is related to the nature of left-right alignment when looking in the mirror.

In order to know the distance between any point on the coordinate axis and the origin. Suppose that we can plot numerical values on the coordinate axis. Then, from the origin to the direction indicated by the coordinate axis, the numerical value is plotted on the coordinate axis every other unit length. The value is the number of descriptions and the positive integer distance from the origin; Similarly, we can also use the direction pointed by the coordinate axis to describe the negative integer distance from the origin. The value depicted on the X axis is called X coordinate, also called abscissa, and the value depicted on the Y axis is called Y coordinate, also called ordinate. Although, here, these two coordinates are integers, corresponding to specific points of the coordinate axis. In proportion, we can generalize to every point of real coordinates and its corresponding coordinate axis. These two coordinates are rectangular coordinates of rectangular coordinate system, marked as.

The position of any point p on the plane can be uniquely represented by rectangular coordinates. As long as a straight line perpendicular to the X axis is drawn from point P, the X coordinate of point P can be obtained from the intersection of this straight line and the X axis. Similarly, you can find the Y coordinate of point P, so that we can get the rectangular coordinate of point P.

Cartesian coordinate system can also be extended to three dimensions and higher dimensions.

The two coordinate axes of rectangular coordinate system divide the plane into four parts, called quadrants, which are numbered ⅰ, ⅱ, ⅲ and ⅳ in Roman numerals respectively. Traditionally, both coordinates of quadrant I are positive values; The x coordinate of quadrant ⅱ is negative and the y coordinate is positive; Both coordinates of quadrant ⅲ are negative; The x coordinate of quadrant ⅳ is positive and the y coordinate is negative. So the number of quadrants is counterclockwise, from quadrant I to quadrant IV.