ShmoopTube

00:04

Plotting points in 3D, a la Shmoop.

00:11

George has been a naughty boy...

00:13

...putting petroleum jelly on all the doorknobs of the house...

00:17

...painting his sister's face with red paint while she was asleep...

00:21

...and all before breakfast.

00:23

Instead of the normal 10-minute timeout, his parents decide to really teach him a lesson...

00:27

...with a three dimensional math problem.

00:29

The problem that he has to plot...

00:33

(3, 2, 1)

00:36

Math isn't George's strongest subject, so let's help him out.

00:41

Before we try figuring out what (3, 2, 1) means...

00:44

...let's first orient ourselves with the axes of a three dimensional coordinate system.

00:49

Think of the x, y, and z axes as the corner of a room, with the x-axis pointing toward you.

00:55

So what does (3,2,1) have to do with anything?

00:58

(3, 2, 1) is an ordered triple in the form (x, y, z).

01:03

Which means that to graph this point, we would go 3 units along the x-axis....

01:08

...2 units along the y-axis... and 1 unit up on the z-axis.

01:14

We first plot the x, y, and z points...

01:17

...3 on the x, 2 on the y, and 1 unit on the z.

01:22

And then we draw dotted lines parallel to the axes and connect the x and y points.

01:28

We then draw dotted lines parallel to connect all the points drawn.

01:32

We can draw a 3D box by projecting dotted lines to the point.

01:36

Ta-da! (3, 2, 1) is where the red dot is.

01:40

It takes him long enough, but George finally finishes plotting these points...

01:43

...and has regained his freedom.

01:45

Although something tells us he's not quite in the clear yet...

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