Coordinate Axes in Two Dimension

In 2 dimensional plane, a point is located using its distance from the two coordinate axes. These axes are perpendicular to each other always. Thus coordinate axes in two dimension helps us determine the position of the point in terms of the length and width of the projections of the point on each coordinate axis.

There are two axis in the two dimension coordinate system,

• X-axis
• Y-axis

X-axis and Y-axis

Cartesian coordinate system in 2 dimensions uses two axes to show a point in 2 dimensional space. These axes are X-axis and Y-axis . These axes are placed perpendicular to each other. X-axis is the horizontal axis and Y-axis is the vertical axis. The point of intersection of X-axis and Y-axis is called Origin.

Each point in the cartesian coordinate system is determined using its x and y coordinate and represented as (x, y). The Origin is represented using O(0, 0). The X-axis is divided into two parts by the origin i.e. OX and OX’. OX’ is used to show numbers with negative X coordinate. Similarly Y-axis is divided into two parts by the origin i.e. OY and OY’. OY’ is used to show numbers with negative Y coordinate.

Quadrants and Sign Convention

The XX’ and YY’ intersect at origin and this results in the formation of 4 quadrants as shown in the below diagram:

• The region XOY is the First Quadrant.
  • In first quadrant, both x and y coordinate are positive i.e . (+, +).
• The region X’OY is the Second Quadrant.
  • In second quadrant, x coordinate is negative and y coordinate is positive i.e. (-, +) .
• The region X’OY’ is the Third Quadrant.
  • In third quadrant, both x and y coordinate are negative i.e. (-, -) .
• The region XOY’ is the Fourth Quadrant.
  • In fourth quadrant, x coordinate is positive and y coordinate is negative i.e. (+, -).

Representing a Point On Coordinate Axes

A point is represented on coordinate axes using its x coordinate and y coordinate. The X coordinate is called abscissa and the Y coordinate is called ordinate. A point P is represented as P(x, y) as shown in the below figure:

In the above figure point P is shown on the Coordinate axes system. The length OR represents the abscissa and length OS represents ordinate of point P.

If the abscissa of a point is zero then it will lie on the YY’ and if the ordinate of a point is zero then it will lie on XX’.

Coordinate Axes are the fundamental of the concept in Coordinate Geometry, which is the amalgamation of two branches of mathematics, i.e., algebra and geometry. The basic idea of coordinate geometry is to study the properties of various figures in mathematics i.e., points, lines, curves, etc.

Thus, Coordinate Axes form the basis of coordinate geometry which is the branch of mathematics dealing with the plotting of points, lines, and curves on the coordinate axes system or the Euclidean plane. In this article, we will learn about the Coordinate Axes in detail.