# Ordered Pair

If you've never encountered an ordered pair before, don't worry:
This concept is relatively straightforward, and as the name implies,
quite orderly. But what exactly *is* an ordered pair? Why might
you need to use ordered pairs in math? Let's find out:

## What exactly IS an ordered pair?

An ordered pair is a set of two numbers contained within brackets often representing a point on the Cartesian plane. Here's an example:

$\left(x,y\right)\to \left(5,2\right)$

The first number represents the "x" value, while the second number represents the "y" value.

"x" represents the horizontal value, while "y" represents the vertical value.

## Other terms for ordered pairs

We often call ordered pairs "rectangular pairs" because when we plot these numbers on a graph, they form a rectangle. You might also hear the term "Cartesian coordinates" in honor of Rene Descartes. Although plotting numbers on a graph might not seem like a big deal, Descartes revolutionized the world of math when he did this for the first time. Why? Because he created a link between algebra and geometry.

## Solving equations with ordered pairs

To help us visualize how ordered pairs connect geometry and algebra, let's solve a simple equation:

$y=x-3$

We can use a graph to see that $\left(5,2\right)$ is a solution to this equation by plugging in 5 for x and 2 for y:

$2=x-3$

Remember, while the "x" value might come second in an equation, it always comes first in the ordered pair.

So what happens to this ordered pair when we put it on a graph? Let's take a look:

If we had an ordered pair of $\left(0,0\right)$ , we would put this point right in the middle of the graph. This location is called the "origin."

## Ordered pairs in other mathematical situations

If this seems a bit easy, don't worry: Ordered pairs can get much more complicated as we get into higher math. For example, an ordered pair might consist of sets, functions, or even other ordered pairs!

Cartesian coordinates can also plot locations in
*three* dimensions instead of just two, such as
$\left(2,3,1\right)$
where instead of x and y, we now have
$\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)$
. The "z" axis comes right out of and into the page to bring the
graph into 3d space.

## Topics related to the Ordered Pair

Word Problems: Plotting Points

## Flashcards covering the Ordered Pair

Common Core: 5th Grade Math Flashcards

## Practice tests covering the Ordered Pair

MAP 5th Grade Math Practice Tests

Common Core: 5th Grade Math Diagnostic Tests

## Get your student started with a qualified math tutor today

If your student is struggling to understand the concepts behind ordered pairs, they may benefit from working with a tutor. You can guide your student towards greater math achievements by contacting Varsity Tutors. We'll find your student someone who can help them understand the math concepts around ordered pairs and beyond. Reach out today, and we'll pair them with a qualified math tutor.

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