A pair of two numbers a and b listed in a specific order is called an ordered pair. The ordered pair (a, b) has a at the first place and b at the second place. To describe the location of a point, we use a definite order. That is,

(i) We start from the origin and first move along the x-axis. If the movement is to the right of the origin, the distance is taken as positive while the movement to the left of the origin gives the negative distance.
(ii) Then, we move along parallel to the y-axis. Again the distance above the x-axis is considered positive and that below it is considered as negative.

Ordered Pair is the representation of two numbers by using parentheses with a certain order. The ordered pair is used to show position on a graph, where the left side value is the x-coordinate(horizontal) value and the right side value is the y-coordinate(vertical) value. It may be positive or negative.

Examples of Ordered Pairs:

(4,2), ( -1,3), (2.5, -5), (0,0), (0,6), (2,3) and (3,2) are some examples of ordered pairs. These are called ordered pairs as the order is important. The pair (2,3) is different from (3,2).

Ordered Pairs

In the figure shown above,

(i) To locate the point A in the plane, we first move a distance of +3 units from O along x-axis. Now, we go up to a distance of +2. Thus, the location of the point A is given by (3, 2)

In the ordered pair (3, 2) the first element (3) is called the x-coordinate or abscissa while the second element (2) is called the y-coordinate or ordinate. The numbers 3 and 2 are called the cartesian coordinates of point A or simply coordinates of A and are written as the pair (3, 2).

Ordered Pairs Example

(ii) Similarly, the coordinates of point B are (2, 3). Here, 2 is the x-coordinate or abscissa and 3 is the y coordinate or ordinate. Both points A(3, 2) and B(2, 3) lie in the first quadrant. Note that the numbers in the ordered pairs representing points in the first quadrant are both positive. That is, the ordered pairs are of the type (+, +).

(iii) To locate point C(-1, 3), we first move 1 unit distance to the left of the origin along x-axis (-1 unit from O along x-axis) and then, go up by 3 units. Thus, the point is represented as C (-1, 3). The ordered pairs in the second quadrant are of the form (-, +).

(iv) To locate the point D(-2, -2), we first move a distance of -2 units from O along x-axis and then go down a distance of -2 units. Point D(-2, -2) lies in the third quadrant. The points in the third quadrant represent ordered pairs of the type (-, -).

(v) Finally, the point E(1, -3) lies in the fourth quadrant. The ordered pairs in the fourth quadrant are of the form (+, -).