Set of Ordered Pairs

In the Cartesian coordinate system, an organised pair contains two numbers represented in a certain order. The ordered pair is written in enclosed brackets. A set of ordered pairs is also termed as a relation. A set of ordered pairs constitutes an x coordinate and a y coordinate.

Set of ordered pairs examples are as follows 

1. (a, b)

2. (5, 9)

3. (1, 7)

Set of ordered pairs definition

The pair of elements or numbers that occur in an organised way and are written in brackets are defined as a set of ordered pairs. 

In a set of ordered pairs, the first element is termed as “the first component or abscissa,” which is the X-coordinate when plotted graphically. Likewise, the second element is termed as “the second component or ordinate,” which is the Y-coordinate when plotted graphically.

Each set of ordered pairs is unique in nature. The components of the set of ordered pairs cannot be interchanged for a set of ordered pairs, i.e., (a, b) ≠ (b, a).

Examples on the set of ordered pairs

1. Find the value of x-coordinate for the ordered pair (3, 5).

For an ordered pair, the first element is the value of ‘X-coordinate.’ Hence, for the ordered pair (3, 5), the value of the x-coordinate is 3.

2. Find the value of x-coordinate for the ordered pair (9, 7).

For an ordered pair, the first element is the value of ‘X-coordinate.’ Hence, for the ordered pair (9, 7), the value of the x-coordinate is 9.

3. Find the value of y-coordinate for the ordered pair (2, 1).

For an ordered pair, the second element is the value of ‘Y-coordinate.’ Hence, for the ordered pair (2, 1), the value of y-coordinate is 1.

4. Find the value of y-coordinate for the ordered pair (3, 4).

For an ordered pair, the second element is the value of ‘Y-coordinate.’ Hence, for the ordered pair (3, 4), the value of y-coordinate is 4.

Set of ordered pairs and the Cartesian plane 

1. Plot (3, 9) on a Cartesian plane. 

For an ordered pair, the first element is the value of ‘X-coordinate,’ and the second element is the value of ‘Y-coordinate.’ 

For (3, 9), X-coordinate value = 3, and Y-coordinate value = 9.

2. Plot (2, 4) on a Cartesian plane. 

For an ordered pair, the first element is the value of ‘X-coordinate,’ and the second element is the value of ‘Y-coordinate.’ 

For (2, 4), X-coordinate value = 2, and Y-coordinate value = 4

3. Plot (1, 5) on a Cartesian plane. 

For an ordered pair, the first element is the value of ‘X-coordinate,’ and the second element is the value of ‘Y-coordinate.’ 

For (1, 5), X-coordinate value = 1, and Y-coordinate value = 5

4. Find the ordered pair from the given Cartesian plane.

For an ordered pair, the first element is the value of ‘X-coordinate,’ and the second element is the value of ‘Y-coordinate.’ In the given Cartesian plane, the value of X-coordinate is 9, and the value of Y-coordinate is 8. Hence, the ordered pair is (9, 8).

5. Find the ordered pair from the given Cartesian plane.

For an ordered pair, the first element is the value of ‘X-coordinate,’ and the second element is the value of ‘Y-coordinate.’ In the given Cartesian plane, the value of X-coordinate is 1, and the value of Y-coordinate is 2. Hence, the ordered pair is (1, 2).

6. Find the ordered pair from the given Cartesian plane.

For an ordered pair, the first element is the value of ‘X-coordinate,’ and the second element is the value of ‘Y-coordinate.’ In the given Cartesian plane, the value of X-coordinate is 9, and the value of Y-coordinate is 1. Hence, the ordered pair is (9, 1).

7. Show the ordered pairs (5, 3) and (3, 5) are different using a Cartesian plane. 

For a set of ordered pairs (a, b) ≠ (b, a). Likewise, (5, 3) ≠ (3, 5). The ordered pairs will have different X-axis and Y-axis values.

Property of set of ordered pairs

Equality of Ordered Pairs

By definition, two ordered pairs are said to be equal if and only if the corresponding first elements are equal and the corresponding second elements are equal.

Consider two sets of ordered pairs (x, y) and (c, d). By the property of equality of ordered pairs, x = c and y = d.

Problems based on equality of ordered pairs

1. Find the value of ‘a’ if (2a+5, b+7) = (7, 9).

According to equality of ordered pairs, 2a+5 = 7

2a = 7 – 5 = 2

2a = 2

a = 1

2. Find the value of ‘b’ if (2a+5, b+7) = (7, 9).

According to equality of ordered pairs, b+7 = 9

b = 9 – 7 = 2

b = 2

3. Find the value of ‘x’ and ‘y’ if (2x+2, 5)   = (8, y-3).

According to equality of ordered pairs, 2x+2 = 8 & 5 = y-3

2x = 6 & y = 5+3

x = 3 & y = 8

Conclusion 

In the above topic, we studied the set of ordered pairs. With the help of its definition and examples, we have mastered the set of ordered pairs. We also learned about different ways to represent a set of ordered pairs. We discovered different properties of the set of ordered pairs. Then, with the help of examples, we learned each type in-depth, and finally, we solved some cases to reinforce our understanding of the concept.