The Cartesian plane, or Cartesian coordinate system, is a two-dimensional (perfectly flat) area that contains a system in which points can be identified by their position using an ordered pair of numbers.

This pair of numbers represents the distance of the points to a pair of perpendicular axes. The axes are called the x-axis (horizontal or abscissa axis) and y-axis (vertical or ordinate axis).

Thus, the position of any point is defined by a pair of numbers in the form (x, y). So x is the distance from the point to the x-axis, while y is the distance from the point to the y-axis.

These planes are called Cartesian, derivative of Cartesius, the Latin name of the French philosopher René Descartes (who lived between the end of the 16th century and the first half of the 17th century). It was this philosopher who developed the blueprint for the first time.

Brief explanation of the characteristics of the Cartesian plane

The Cartesian plane has infinite extension and orthogonality on the axes

Both the x-axis and the y-axis extend infinitely through both ends, and intersect each other perpendicularly (at a 90 degree angle). This feature is called orthogonality.

The point where both axes intersect is known as the origin or zero point. On the x-axis, the section to the right of the origin is positive and to the left is negative. On the y-axis, the section above the origin is positive and below it is negative.

The Cartesian plane divides the two-dimensional area into four quadrants

The coordinate system divides the plane into four regions called quadrants. The first quadrant has the positive part of the x-axis and the y-axis.

For its part, the second quadrant has the negative part of the x-axis and the positive part of the y-axis. The third quadrant has the negative part of the x-axis and the negative part of the y-axis. Finally, the fourth quadrant has the positive part of the x-axis and the negative part of the y-axis.

The locations on the coordinate plane are described as ordered pairs

An ordered pair tells the location of a point by relating the location of the point along the x-axis (the first value of the ordered pair) and along the y-axis (the second value of the ordered pair).

In an ordered pair, such as (x, y), the first value is called the x coordinate and the second value is the y coordinate. The x coordinate is listed before the y coordinate.

Since the origin has an x ​​coordinate of 0 and a y coordinate of 0, its ordered pair is written (0,0).

The ordered pairs of a Cartesian plane are unique

Each point on the Cartesian plane is associated with a unique x coordinate and a unique y coordinate. The location of this point on the Cartesian plane is final.

Once the coordinates (x, y) for the point have been defined, there is no other with the same coordinates.

The Cartesian coordinate system represents mathematical relationships

The coordinate plane can be used to plot graph points and lines. This system allows to describe algebraic relationships in a visual sense.

It also helps create and interpret algebraic concepts. As a practical application of everyday life, positioning on maps and cartographic plans can be mentioned.

References

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5. Monterey Institute. (s / f). The Coordinate Plane. Retrieved on January 10, 2018, from montereyinstitute.org.