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# 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 $\left(x,y,z\right)$ . The "z" axis comes right out of and into the page to bring the graph into 3d space.

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