Mathematical functions can be expressed graphically on a Cartesian plane , as long as we express the relationship between a variable x and a variable and in such a way that it can be solved.įor example, if we have a function that states that the value of y will be 4 when that of x is 2, we can say that we have an expressible function like this: y = 2x. Functions in a Cartesian plane Functions can be expressed graphically in the Cartesian plane. Thus, with respect to the origin or point 0, the right segment of the “x” axis is positive, while the left is negative. Consequently, the rising segment of the “y” axis is positive, while the descending segment is negative. The origin is called the point at which the “x” and “y” axes intersect, the point to which the value of zero (0) is assigned. For this reason, it is also known as the zero point (point 0). Each axis represents a numerical scale that will be positive or negative according to its direction with respect to the origin. Ordinate : the ordinate axis is oriented vertically and is represented by the letter “y”.Abscissa : the abscissa axis is arranged horizontally and is identified by the letter “x”.Coordinate axesĬoordinate axes are called the two perpendicular lines that interconnect at a point in the plane. These lines are called the abscissa and the ordinate. So, The elements and characteristics that make up the Cartesian plane are the coordinate axes, the origin, the quadrants, and the coordinates. Each point is expressed in their respective coordinates , always saying first the abscissa and then the ordinates. Joining two points you can build a line, and with several lines a figure. The Cartesian plane is composed of two perpendicular axes, as we know: the ordinate ( y axis ) and the abscissa ( x axis ) . Both lines extend to infinity, both in their positive and negative values. The only crossing point between the two is called origin (coordinates 0,0) .įrom the origin each axis is marked with values expressed in whole numbers. The intersection point of any two points is called a point. These values can be positive or negative, depending on their location with respect to the lines that make up the plane. In the coordinate system, to locate the points we need two values: the first corresponding to the horizontal axis X and the second to the vertical axis Y , which are denoted in parentheses and separated by a comma: (0,0) for example, is the point where both lines intersect. There are two ways to resolve these operations: mathematically and then graph it, or we can find a solution graphically, since there is a clear correspondence between what is illustrated on the Cartesian plane, and what is expressed in mathematical symbols. In addition, it allows to draw two-dimensional geometric figures from straight lines and curves. These figures correspond to certain arithmetic operations , such as equations, simple operations, etc. The Cartesian plane is a diagram in which we can locate points, based on their respective coordinates on each axis, just as a GPS does on the globe. From there, it is also possible to graphically represent the movement (the movement from one point to another in the coordinate system). What is the Cartesian plane for? The coordinates allow you to locate points in the Cartesian plane. The Cartesian plane owes its name to the French philosopher René Descartes (1596-1650), creator of the field of analytical geometry. It is a two-dimensional system, consisting of two axes that extend from an origin to infinity (forming a cross). These axes are intercepted at a single point (denoting the point of origin of coordinates or point 0.0).Ī set of length marks are drawn on each axis, which serve as a reference to locate points, draw figures or represent mathematical operations . That is, it is a geometric tool to put the latter in relation graphically. It is used to graphically represent mathematical functions and analytical geometry equations . It also allows to represent relationships of movement and physical position. What is the Cartesian plane?Ī Cartesian plane or Cartesian system is called an orthogonal coordinate diagram used for geometric operations in the Euclidean space (that is, the geometric space that meets the requirements formulated in ancient times by Euclid). In addition, how functions are represented. We explain what the Cartesian plane is? how it was created, quadrant in cartesian plane with elements.