In coordinate geometry, we represent the coordinate of any point or object as (a,b), where a is the length on the x-axis and b is the length on the y-axis. These x and y axes are called abscissa and ordinate, respectively. It is usually the second component in the coordinate geometry when it is denoted in pairs. Cartesian coordinates are represented on a graph or map, where these coordinates denote the location of any object or point. These Cartesian coordinates represent the distance of the point from the origin.
For example, if the location of a point is denoted by (5,8) in Cartesian coordinate geometry, then 5 is the abscissa, and 8 is the ordinate. The point is located at a distance of 5 units from the origin on the x-axis and 8 units from the y-axis. In order to locate these points on a graph or map, we need to move 5 units on the x-axis (horizontally) and 8 units on the y-axis (vertically) and locate the point on the intersection of these two lines.
The ordinate is usually the secondary axis. For example, if you plot a map with the y-axis as the central axis and the x-axis as a secondary axis, then the x-axis will become the ordinate. It is the absolute distance between the origin of Cartesian geometry and the projection. The sign of an ordinate depends upon the location of the object or point on the Cartesian plane. If the point or object is located above and to the right of the axes, then they will be positive. If they are down and towards the left, then they will be negative.
The signs of abscissa and ordinate change with their locations in different quadrants. The table is given as under-.
Quadrant | Sign |
I | Positive |
II | Positive |
III | Negative |
IV | Negative |
Abscissa | Ordinate |
It is the value on the x-axis in a coordinate plane. | It is the value on the y-axis on a coordinate plane. |
It is perpendicular to the y-axis. | It is perpendicular to the x-axis. |
Abscissa is the horizontal distance of an object or point, if the primary axis is horizontal. | Ordinate is the vertical distance of an object or point, if the main axis is horizontal. |
Example – (5,-6) – In this, 5 is the abscissa and is on the positive side of the axis. | Example – (5,-6) – In this, -6 is the ordinate, placed on the negative side of the axis. |
1. The term abscissa was firstly used by Fibonacci around 1220 to denote a cut-off line.
2. The term ordinate comes from the Latin phrase ‘linea ordinate applicata,’ which means the applied lines are parallel.
3. The Cartesian system was made by Rene Descartes, who was a renowned mathematician. He used this system to represent the location of an object or point in space and plane both.
4. Unlike a two-dimensional world or Cartesian plane, if an object is represented in space, three axes come into the picture, viz. (x,y,z). Here, x is the length along the x-axis, y along the y-axis, and z along the z-axis from the origin.