To know the ordered pair of a coordinate system let us recall the coordinate system.
We represent a point in a plane by ordered pairs of real numbers called the Cartesian co-ordinates. To determine the position of a point in a plane we draw two mutually perpendicular straight lines XOX’ and YOY’.
XOX’ is called the x-axis which is a horizontal line.
YOY’ is called the y-axis which is a vertical line.
Point O is called the origin.
Whenever we write the co-ordinates of a point, first we write the x- co-ordinate, and then we write the y-co-ordinate. Suppose a and b is a pair of two numbers which is listed in a specific order then the co-ordinates (a, b) are called the ordered pair.
Thus, in (a, b) we notice a is at the first place so it is known as x- co-ordinate and b at the second place so it is known as y- co-ordinate.
In an order pair, if the order of the numbers is changed then it represents a different point,
Hence, (a, b) ≠ (b, a)
Thus, (5, 4) ≠ (4, 5)
Examples of ordered pair of a coordinate system:
1. In an ordered pair (3, 5): x co-ordinate is 3 and y co-ordinate is 5
But in an ordered pair (5, 3) x co-ordinate is 5 and y co-ordinate is 3
So, we observe that (3, 5) and (5, 3) represent different points.
2. In an ordered pair (7, 2) x co-ordinate is 7 and y co-ordinate is 2
But in an ordered pair (2, 7) x co-ordinate is 2 and y co-ordinate is 7
So, we observe that (7, 2) and (2, 7) represent different points.
The co-ordinate of the origin are (0, 0) i.e., its x co-ordinate is 0 and its y co-ordinate is also 0.