# Ordered Pair

## What are Ordered Pair?

The arrangements of two number inside a bracket is called ordered pair.

For Example
(4, 7), (10, 3), (-2, 11) are all examples of ordered pair.

The first place in the ordered pair is called Abscissa.
The second place is known as Ordinate.

Ordered pair is important source of following information.

⟹ The abscissa tells the distance of point from x axis.

⟹ The ordinate tells the distance of point from y axis.

Ordered Pair is very important concept in coordinate geometry.

We know that cartesian plane is divided into x & y axis.
The horizontal line of cartesian plane is known as x axis.
The vertical line is known as y axis.

Given above is the x-y cartesian plane.

Let us consider a ordered pair (2, 3) as an example.

The pair (2, 3) gives us following information;

Abscissa is 2, It means that distance from x axis is 2 units.

Ordinate is 3, it means that distance from y axis is 3 units.

Plotting the ordered pair in cartesian plain.

In above image, point A shows the location of ordered pair (2, 3)

Conclusion
Ordered pair tells the location of point in cartesian plane.

## Comparing two ordered Pair

First of all keep in mind that ordered pair is not a set which contains two elements.

The ordered pair contain elements which shows the location of point in cartesian plane.

Now consider two ordered pairs.
A = ( 2, 3 ) and B = ( 3 , 2 )

Though both the ordered pairs are made of same elements 2 & 3 but they are not equal to each other.

In ordered pair A= (2, 3)
⟹ Distance of point from x axis is 2 units
⟹ Distance from y axis is 3 units.

In Ordered pair B = ( 3, 2 )
⟹ Distance of point B from x axis is 3 units
⟹ Distance from y axis is 2 units.

Hence, both point A & B are situated in different location.
Below is the image showing location of point A & B.

Hence, both the point A & B are not same.

### Equal Ordered Pairs

Two ordered pairs are equal when;
⟹ both pairs have same abscissa, and;
⟹ both pairs have same ordered pairs.

For Example;
Consider the two ordered pairs P & Q
P ( 5 , 7) and Q (5, 7)

Here the pairs P & Q are equal ordered pairs since;
⟹ Both have same abscissa ( 5 units )
⟹ Both have same ordinates ( 7 units )

### Ordering of Ordered Pairs

In ordered pairs, the ordering of the two elements cannot be changed.

For example,
The ordered pair (5, 7) cannot be written as (7, 5).

Note that the pairs (5, 7) and (7, 5) are completely different ordered pair situated in different location in cartesian plane.

Given below is the location of pair (5, 7) and (7, 5).

Conclusion
We cannot change the location of elements in ordered pairs.

## Difference between Sets and Ordered Pairs

Both sets and ordered pairs are completely different from each other.

(i) Set is just a collection of different elements.
Ordered pairs tells the location of point in cartesian plane.

(ii) Elements in a set can be repeated.
Set A = { 2, 5 } can be written as Set A = {2, 2, 5, 5}

In ordered pairs the elements of the pair cannot be repeated.

(iii) The position of elements in the set can be interchanged.

In ordered pairs, the position of numbers cannot be interchanged.

Conclusion
Set and Ordered pairs are completely different phenomenon.
There should be no comparison between the two.

## Solved Examples – Ordered Pairs

(01) Locate the abscissa and ordinate of below ordered pairs.

Solution
The first element which tells the distance from x axis is called Abscissa.

The second element which tells the distance from y axis is called ordinate.

(i) (2, 5)
Abscissa is 2.
Ordinate is 5

(ii) (3, 7)
Abscissa is 3.
Ordinate is 7.

(iii) (10, 2)
Abscissa is 10.
Ordinate is 2.

(iv) (13, 9)
Abscissa is 13.
Ordinate is 9

(02) Consider the two ordered pairs A & B.

Check if the ordered pairs A & B are equal or not.

Solution
Equal ordered pairs have same abscissa and ordinate.

In the given ordered pairs, abscissa is same but ordinate is different.
Hence A & B are not equal.

(03) If below ordered pairs are equal then find the value of a and b.

Solution
Since both the ordered pairs are equal they have same abscissa and ordinate.

Both (7, b) & ( a, 13) have same abscissa.
So, a = 7

They also have same ordinate.
So, b = 13

(04) Given below are two equal ordered pairs. Find the value of a & b.

Solution
Since the ordered pairs are equal they have same abscissa and ordinate.

Since abscissa are equal, we can write;
2a – 7 = -3a +3

2a + 3a = 7 +3

5a = 10

a = 10/5

a = 2

So the value of a is 2.

We also know that ordinates are also equal.
3b – 6 = 3

3b = 3 + 6

3b = 9

b = 9/3

b = 3

Hence, the value of b is 3