WHAT ARE THE PARTS OF THE CARTESIAN PLANE? - MATHS - 2025

The parts of the Cartesian plane are composed of two real, perpendicular lines, which divide the Cartesian plane into four regions. Each of these regions is called quadrants, and the elements of the Cartesian plane are called points. The plane, along with the coordinate axes, is called the Cartesian plane in honor of the French philosopher René Descartes, who invented analytical geometry.

The two lines (or coordinate axes) are perpendicular because they form an angle of 90º between them and they intersect at a common point (origin). One of the lines is horizontal, being called the origin of the x (or abscissa) and the other line is vertical, being called the origin of y (or ordinate).

Kbolino / Public domain

The positive half of the X axis is to the right of the origin and the positive half of the Y axis is up from the origin. This allows the four quadrants of the Cartesian plane to be distinguished, which is very useful when plotting points on the plane.

Points of the Cartesian plane

Each point P on the plane can be assigned a pair of real numbers which are its Cartesian coordinates.

If a horizontal line and a vertical line pass through P, and they intersect the X axis and the Y axis at points a and b respectively, then the coordinates of P are (a, b). (A, b) is called an ordered pair, and the order in which the numbers are written is important.

The first number, a, is the "x" coordinate (or abscissa) and the second number, b, is the "y" coordinate (or ordinate). The notation P = (a, b) is used.

It is evident from the way in which the Cartesian plane was constructed that the origin corresponds to the coordinates 0 in the "x" axis and 0 in the "y" axis, that is, O = (0,0).

Quadrants of the Cartesian plane

As can be seen in the previous figures, the coordinate axes generate four different regions that are the quadrants of the Cartesian plane, which are denoted by the letters I, II, III and IV and these differ from each other in the sign that the points have that are in each of them.

Quadrant

The points of quadrant I are those that have both coordinates with a positive sign, that is, their x coordinate and their y coordinate are positive.

For example, the point P = (2,8). To graph it, point 2 is located on the "x" axis and point 8 on the "y" axis, then the vertical and horizontal lines are drawn respectively, and where they intersect is where point P is.

Quadrant

The points in quadrant II have a negative "x" coordinate and a positive "y" coordinate. For example, the point Q = (- 4,5). It is graphed proceeding as in the previous case.

Quadrant

In this quadrant, the sign of both coordinates is negative, that is, the "x" coordinate and the "y" coordinate are negative. For example, the point R = (- 5, -2).

Quadrant

In quadrant IV the points have a positive "x" coordinate and a negative "y" coordinate. For example the point S = (6, -6).

References

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