Graphing Points & Lines in Three Dimensions

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  • 0:00 Three Dimensions
  • 1:10 Graphing a Point
  • 2:31 Graphing a Line/Plane
  • 4:11 Example
  • 4:31 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will know how read the three coordinates given to you and graph any given point in the three-dimensional coordinate space. Then test your knowledge with a quiz.

Three Dimensions

Plotting points and graphing lines in two-dimensions is easy because you can simply draw it on a flat piece of paper. Whatever you draw on that sheet of paper will be two-dimensional. It only has length and width. For points on the coordinate plane, they only have an x component and a y component. But, what happens when you add in a third component, a z component? What then? Welcome to the coordinate space, a place where you can plot three-dimensional points and graph three-dimensional lines.

We define three-dimensional space as that space where you have a width, a length, and a height. In coordinate space, this translates to having an x component, a y component, and a z component. Why do you need to know how to plot points and graph in three-dimensions? You need to know how to do this because you will be tested on this subject in your standardized tests that you take for college. Also, you need to know this information if you want to get involved with computer aided design (or CAD) as the objects in CAD images are sometimes drawn in the three-dimensional space.

Graphing a Point

So first, let's consider plotting a single point in three-dimensions

Imagine that you are beginning to design something used a computer aided design program such as SketchUp. You are looking at the three-dimensional space. The point that you want to plot is (4, 2, 1). Breaking this point down to its components, this point is telling you that its x component is 4, its y component is 2, and its z component is 1. To plot points in the three-dimensional coordinate space, you do it pretty much like you would in the two-dimensional plane, except you add another dimension. The third dimension tells you how high your point is. If your third dimension happens to be negative, then you will be going lower instead of higher. Your point is no longer always at ground level. It can now float! To graph this point, you first find your x component on the x-axis. Then you follow this line to your y component on the y-axis. Then you go up until you've reached your z component. So, your point (4, 2, 1) is the point (4, 2) at a height of 1.

3d graph

Looking at this graph, notice that your axes are in different locations. Your axis that goes up and down is now the z axis. The x axis here is now going diagonal. We need to draw it like this because we are trying to fit three dimensions into two.

Graphing a Line/Plane

Next, let's see about graphing a linear equation in three dimensions. When you graph a liner equation in three dimensions, you won't get a straight line like you would when graphing in two dimensions. Instead, you will get a plane, an endless flat surface. Let's take a look.

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