# How to Plot Points in Three Dimensions Video

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• 0:04 Three Dimensions
• 0:47 Plotting Points in 3D
• 2:24 Another Example
• 3:17 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we'll look at what a three-dimensional coordinate system looks like. After that, we'll learn how to plot points in three dimensions and look at a couple of examples of the process.

## Three Dimensions

You may be familiar with the two-dimensional coordinate plane like the one appearing here, in which there is an x-axis and a y-axis.

However, we don't live in a two-dimensional world! Take a moment to find a corner where two walls and the floor meet. Notice the floor is a two-dimensional plane and we can consider the lines where the floor meets the walls the x-axis and the y-axis. Now, consider the line where the walls meet. This line adds in a new axis to the two-dimensional coordinate plane. If we call this line the z-axis, we now have three axes and we're now working in three dimensions. You probably never looked at a corner in this way before, huh?

## Plotting Points in Three Dimensions

As we just saw from our corner example, when it comes to working in three dimensions, we simply add an axis to the two-dimensional coordinate plane. We have an x-axis, y-axis, and z-axis, all intersecting at 0.

In the same way that we can plot a point on the two-dimensional coordinate plane, we can also plot a point in three dimensions. It just takes one extra step!

First of all, let's look at how we plot a point, (x, y), on the two-dimensional coordinate plane:

1. Locate x on the x-axis
2. From that point, moving parallel to the y-axis, move y units; this is your point

Now, let's take a look at when we are working in three dimensions. To plot the point (x, y, z) in three-dimensions, we simply add the step of moving parallel to the z-axis by z units. That is, to plot a point (x, y, z) in three dimensions, we follow these steps:

1. Locate x on the x-axis
2. From that point, moving parallel to the y-axis, move y units
3. From that point, moving parallel to the z-axis, move z units; this is your point

Well, that doesn't seem so hard. For example, assume we want to plot the point (1, 2, 3) in three dimensions:

• First, we locate 1 on the x-axis
• Next, from that point, we move 2 units parallel to the y-axis
• Lastly, from that point, we move 3 units parallel to the z-axis

And there we have it. We've plotted our point!

## Another Example

Let's consider another example of this. Suppose you place an imaginary three-dimensional coordinate system in your house. In doing so, you can represent any location in your house with a point.

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