An ordered pair is a pair formed by two elements that are separated by a comma and written inside the parantheses. For example, (x, y) represents an ordered pair, where 'x' is called the first element and 'y' is called the second element of the ordered pair. These elements have specific names according to what context they are being used and they can be either variables or constants. The order of the elements has a certain importance in an ordered pair. It means (x, y) may not be equal to (y, x) all the time.
(2, 5), (a, b), (0, 5), etc are some examples of ordered pairs.
Graphing Ordered Pairs
Now, we understood the difference between the xcoordinate and ycoordinate of an ordered pair in coordinate geometry. Let us now see the steps to graph ordered pairs.
In these steps, x and y represent the absolute values of x and y respectively.
Example: Graph the ordered pair (4, 3).
Let's start from the origin, move to the right by 4 units (as 4 is positive) and then move down by 3 units (as 3 is negative).
The order of the elements in an ordered pair is important and hence the name "ordered" pair. For example, (4, 3) and (3, 4) are located at different positions on the plane as shown below.
We can see in the above figure that the coordinate plane is divided into 4 parts by the x and y axes. Each of these 4 parts is known as a quadrant. The signs of x and y in an ordered pair (x, y) of a point differs depending upon the quadrant and they are shown in the table below.
For example, (2, 4) refers to 2 on the xaxis (positive) and 4 on the yaxis (negative). So (2, 4) is a point in quadrant IV.
Examples:
For any two ordered pairs (x, y) and (a, b) (either in coordinate geometry or in relations), if (x, y) = (a, b) then x = a and y = b. i.e., if two ordered pairs are equal, then their corresponding elements are equal. This is called "equality property of ordered pairs". For example:
Important Notes on Ordered Pairs:
Ordered Pair Examples
Example 1: Plot the point with the ordered pair (2, 3). State the quadrant in which it lies.
To plot the point (2, 3):
 Move 2 units left from the origin (as 2 is negative)
 Thereby, move 3 units to up (as 3 is positive)
 Place a dot where you have reached.
Then the point on the graph looks like this.
We have plotted (2, 3) and it lies in the Quadrant II.
Example 2: Find the values of x and y if (2x  3, 3y + 2) = (5, 8).
It is given that (2x  3, 3y + 2) = (5, 8).
By the equality property of ordered pairs,
2x  3 = 5 ... (1)
3y + 2 = 8 ... (2)
From (1),
2x = 8 (or) x = 4
From (2),
3y = 6 (or) y = 2
x = 4 and y = 2.
Example 3: Identify the quadrants in which the following ordered pairs lie without plotting them.
(a) (2, 3)
(b) (2, 3).
In (2, 3), xcoordinate is positive and ycoordinate is negative. So it lies in Quadrant IV.
In (2, 3), both x and y coordinates are negative. So it lies in Quadrant III.
(a) lies in IV (b) lies in III.
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