Plotting Points in Three Dimensions

In this module we will cover how to plot three-dimensional graphs. Some examples are shown below.

It becomes necessary to be able to examine three-dimensional shapes because most items in the real-world are three dimensional. Graphing with an x-y coordinate plane only gives us the ability to work with two-dimensional objects. That's great for squares and circles, but what about Rectangular Prisms or Spheres?
Therefore, three-dimensional graphing was created.

The difference between 2D and 3D Graphing is:
2D graphing uses (x, y) ordered pairs that correspond to an x-y axis. 3D graphing uses 3 ordered pairs represented as (x, y, z) which correspond to an x-y-z coordinate plane, shown below.

The (x, y, z) Coordinate Plane

---

The x-y-z axis is similar to the x-y coordinate axis, as the x-and y-axis are still a part of the graph. Instead of it facing at you like the 2D graph does, in 3D, the x-and y-axis are horizontal or flat, the z-axis is the vertical axis.

Graphing Ordered Pairs

---

Just as with 2D graphing, 3D graphing has 3 axes that each correspond with its ordered pair.

To plot the
1. x-coordinate: move forward if it is positive or backwards if it is negative.
2. y-coordinate: move right if it is positive, left if its negative.
3. z-coordinate: move up if it is positive and down if it's negative.
4. Then place a dot at the final location; after all three moves are made. Follow the picture which has the axes labeled with x, y, and z. The ordered pairs correspond to their axes.

   ---

Always start with your pencil at the Origin (0, 0, 0).

Example 1: Plot the point (4, 0, 0).

Example 2: Plot the point (0, 3, 0).

Example 3: Plot the point (0, 0, 4).

Example 4: Plot the point (-3, 0, 0).

Example 5: Plot the point (0, -4, 0).

Example 6: Plot the point (0, 0, -3).

Example 7: Plot the point (2, 3, 4).
Forward 2, right 3, up 4

Example 8: Plot the point (4, 2, -4).
Forward 4, right 2, down 4

Example 9: A 3D plot of a cube

Example 10: A 3D plot of a pyramid