Ordered Pair
Ordered Pair
Simply, an ordered pair is a pair of numbers which are used to locate the point on a coordinate plane. Ordered pairs are also used to show the position on a graph where the horizontal value (x') is the first and vertical value (y') is second. If the ordered pairs have two elements, it is written in the form (x, y) in which x is fixed as the second component. For example,
We can pair off the elements and member diagrammatically as follows: 
Elements  Numbers 
x  20 
y  30 
z  40 
We have drawn an arrow from the elements to the numbers. Such figure is called a balloon diagram or arrow diagram. The arrows are used to show the relationship between the ordered pairs.
Equity of Ordered Pairs
When the first component and the second component of an ordered pair are correspondingly equal then it is called equality of ordered pairs. For examples,
(x, y) = (x, y)
(2, 5) = (2, 5)
(1, 2) = (1, 2)
(4, 5) = (\(\frac{8}{2}\), \(\frac{10}{2}\))
Cartesian Product
Cartesian product is simply defined as the set of all possible ordered pairs with first element x and second element y.
Mathematically, the cartesian product of two sets X and Y is written as,
X × Y = {(x, y) ; x ∈ X and y ∈ Y}
Tree diagram representation of a Cartesian Product
The cartesian product can be represented in 3 ways. They are as follows:
 Tree Diagram
 Mapping Diagram
 Graphical Representation
Tree Diagram
The tree diagram can be represented as follows:
Let, suppose two sets X = (x, y, z) and Y = (3, 4).
Now, Taking xcomponent from set x and ycomponent from set y, then we can do all possible pairs as given below:
\(\therefore\) X × Y = {(x, 3), (x, 4), (y, 3), (y, 4), (z, 3), (z, 4)}
Similarly, we can find the cartesian product B × A as follows:
B × A = {(3, x) (3, y) (3, z) (4, x) (4, y) (4, z)}
Mapping Diagram
Mapping diagram can be represented as given below:
X= {3, 4} and Y = {5, 6}
X×Y = {3, 4} × {5,6} = {(3, 5) (3, 6) (4, 5) (4, 6)}
Here, Each arrow represented an ordered pairs of A × B.
Graphical Representation
Graphical representation can be represented as below:
Suppose, X = {1, 2, 3} and Y = {2, 4, 6}
Then {X×Y} = {1, 2, 3} × {2, 4, 6} = {(1, 2), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 2), (3, 4), (3, 6)}
 An ordered pair is a pair of numbers which are used to locate the point on a coordinate plane.
 When the first component and the second component of an ordered pair are correspondingly equal then it is called equality of ordered pairs.
 The set of all possible ordered pairs with first element and second element y is called Cartesian Product.
 The arrows are used to show the relationship between the ordered pairs.

Find the values of a and b.
(a1, b)= (2, 3)
a=2, b=5
a=4, b=2
a=5, b=3
a=3, b=3

Find the values of a and b.
(a+3, b4) = (0, 5)
a= 3, b=9
a= 2, b= 3
a=3, b=6
a=2, b= 2

Find the values of a and b.
(2a3, 4) = (4a, b+5)
a= 2, b=4
a= 3, b= (frac{2}{3})
a=2, b=4
a= (frac{3}{2}), b= 1

Given pairs are equal. Find x and y.
(6, y) and (x, 5)
x=6, y=6
x=5, y=5
x=5, y=6
x=6, y=5

For what value of x and y, (x+5, y+2) and (7, 5) are equal to each other.
2,2,
3,2
2,3
3,3

For what value of a and b, (a+5, b+2) and (7, 5) are equal to each other.
3,3
2,3
2,2
3,2

For what value of a and b, (2a+5, b+2) and (7, 4) are equal to each other.
2,1
1,1
2,2
1,2

For what value of a and b, (3a4, b2) and (a+8, 2b5) are equal to each other.
6,6
3,3
3,6
6,3

For what value of a and b, (2a+5,b+2 ) and (a+7, 2b5) are equal to each other.
7,2
2,7
2,2
7,2

Find the value of and b.
(2a1, b+2) = (1, 2)
1,0
3,4
3,3
4,4

Find the value of and b.
(a+b, ab) = (8,0)
2,2
2,4
3,3
4,4

Find the value of and b.
(a+b, b+3) = (6, 2b)
2,2
3,3
3,4
4,4

Given pairs are equal. Find the value x and y.
(3x+2, 2y+1) and (5, 3)
2,1
1,1
1,2
2,2

You scored /13
Any Questions on Ordered Pair ?
Please Wait...
Discussions about this note
Forum  Time  Replies  Report 


Jan 05, 2017 
0 Replies View Replies 