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.

## What is an Ordered Pair?

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).

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).

(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 (+, -).

Ordered pairs can be plotted as points on a coordinate plane. The coordinate axes divide the plane of the graph paper into four regions called quadrants.

• Region XOY is named as the first quadrant
• Region YOX' is named as the second quadrant
• Region X'OY' is named as the third quadrant
• Region Y'OX is named as the fourth quadrant
The X-coordinate is called as the abscissa and the Y-coordinate is called as ordinate.
• In the first quadrant, both the abscissa and the ordinate are positive.
• In the second quadrant, the abscissa is negative and the ordinate is positive.
• In the third quadrant, both the abscissa and the ordinate are negative.
• In the fourth quadrant, the abscissa is positive and the ordinate is negative.

The coordinates of origin are (0, 0).

The y-coordinate of every point on the x-axis is 0.

The x-coordinate of every point on the y-axis is 0.

### Examples on Ordered Pair Quadrants

Given below are some examples on ordered pairs quadrants.

Example 1:

Identify the quadrant for the point (4, -5)?

Solution :

Given point (4, -5) has x-coordinate 4 units and y-coordinate -5 units.

So, it is in the fourth quadrant.

Example 2:

Identify the quadrant for the point (-3, -4)?

Solution:

Given point (-3, -4) has x-coordinate -3 units and y-coordinate -4 units

So, it is in the third quadrant.

## Finding Ordered Pairs

The process of finding the ordered pairs is a single step process. For example, let X'OX and YOY' be the coordinate axes. Let P be a point on the graph paper such that P is at a distance of 'a' units from the y-axis and 'b' units from the x-axis. Then, we say that the coordinates of P are P(a, b).

Here a is called the x-coordinate or abscissa of P, while b is called the y-coordinate or ordinate of P. This is the process of finding ordered pairs.

### Examples on Finding Ordered Pairs

Given below are some examples on finding ordered pairs.

Example 1:

Find the coordinates of point "A" as an ordered pair?

Solution:

Given point A is 6 units to the right of the origin and 4 units up from the origin.
We can say that, point A has x-coordinate 6 and y-coordinate 4
So, the answer is (6, 4)

Example 2:

Find the coordinates of each point as an ordered pair?

Solution:

Point A is 8 units to the right of the origin and 8 units up from the origin.
Thus, we can say that, point A has x-coordinate 8 and y-coordinate 8
So, the answer is A(8, 8)

Point B is -8 units to the left of the origin and 8 units up from the origin.
Thus, we can say that, point B has x-coordinate -8 and y-coordinate 8
So, the answer is B(-8, 8)

Point C is -4 units to the left of the origin and -2 units down from the origin.
Thus, we can say that, point C has x-coordinate -4 and y-coordinate -2
So, the answer is C(-4, -2)

Point D is 2 units to the right of the origin and -4 units down from the origin.
Thus, we can say that, point D has x-coordinate 2 and y-coordinate -4
So, the answer is D(2, -4)

## Graphing Ordered Pairs

In general, the 1st coordinate of a plotting point is known as the x - coordinate, which is referred as the horizontal distance from the origin to the plotting point. And, the 2nd coordinate of a plotting point is known as y - coordinate, which is referred as the vertical distance from the origin to the plotting point.

### Examples on Plotting Points on a Graph:

Given below are some examples that explain how to plot points on a graph.

Example 1:

Plot the points A(3,5) B(-5,4) C(-6,-2) and D(3.5,-4.5) on a graph sheet.

Solution:

In the point A(3,5), the x coordinate is 3 and the y coordinate is 5. A distance equal to 3 units is measured starting from the origin along the X-axis. From there, a distance of 5 units is measured in a vertical direction to reach the point A and is marked with a circle.

The other points are plotted similarly. If the X coordinate is positive, distance is measured by moving to the right and when it is negative distance is measured by moving to the left. Similarly, positive Y values are measured up and negatives moving down.

Example 2:

Plot the series of points (-4,0), (-2,0), (2,0) and (4,0). Similarly, plot the second series (0,-3), (0,-1), (0,1) and (3,0). Identify the pattern displayed by both.

Solution: