The video will show you how to plot points in 3D using the axes of the 3D coordinate system. Make sure you're wearing your special glasses for this one.
|Algebra||Coordinates and Graphs|
|Calculus||Points, Vectors, and Functions|
|Points, Vectors, and Functions||Vectors|
Instead of the normal 10-minute timeout, his parents decide to really teach him a lesson...
...with a three dimensional math problem.
The problem that he has to plot...
(3, 2, 1)
Math isn't George's strongest subject, so let's help him out.
Before we try figuring out what (3, 2, 1) means...
...let's first orient ourselves with the axes of a three dimensional coordinate system.
Think of the x, y, and z axes as the corner of a room, with the x-axis pointing toward you.
So what does (3,2,1) have to do with anything?
(3, 2, 1) is an ordered triple in the form (x, y, z).
Which means that to graph this point, we would go 3 units along the x-axis....
...2 units along the y-axis... and 1 unit up on the z-axis.
We first plot the x, y, and z points...
...3 on the x, 2 on the y, and 1 unit on the z.
And then we draw dotted lines parallel to the axes and connect the x and y points.
We then draw dotted lines parallel to connect all the points drawn.
We can draw a 3D box by projecting dotted lines to the point.
Ta-da! (3, 2, 1) is where the red dot is.
It takes him long enough, but George finally finishes plotting these points...
...and has regained his freedom.
Although something tells us he's not quite in the clear yet...