Graphing points in three variables
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Graphing Points in Three Variables. AII, 2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

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Graphing Points in Three Variables

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Graphing points in three variables

Graphing Points in Three Variables

AII, 2.0: Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

LA, 6.0: Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions


Graphing points in three variables1

Graphing Points in Three Variables

Objectives

Key Words

Three-dimensional coordinate system

Z-axis

Ordered triple

Origin (0,0,0)

Octanes

xz-plane

yz-plane

xy-plane

  • Describe the location of each point in relation to the origin

  • Write the coordinates of each point

  • Plot points in three dimensions


Pre requisite check

Pre-requisite Check

Graph an ordered pair (x,y)

  • (4,2)

  • (-2,3)

  • (-3,-1)

  • (1,-4)


Describe the location of each point in relation to the origin

Describe the location of each point in relation to the origin

For the x-axis:

Positive Direction: Move Forward

Like jumping out of the paper

Negative Direction: Moving Back

Like going behind the paper

For the y-axis:

Positive Direction: Moving Right

Negative Direction: Moving Left

For the z-axis:

Positive Direction: Moving Up

Negative Direction: Moving Down


Write the coordinates of each point

Write the coordinates of each point

(1,-4,3)

It takes a few steps to solve these types of problems:

What direction is it moving on the x-axis?

How much? This is you x value.

What direction is it moving on the y-axis?

How much? This is you y value.

What direction is it moving on the z-axis?

How much? This is you z value.

Write the ordered triple (x,y,z)


Plot points in three dimensions

Plot points in three dimensions

Example:

Mark the x value direction

Mark the y value direction

Find the point of intersection

Travel the z value direction (upward or downward)

Plot the point.


Conclusions

Conclusions

Summary

Assignment

To be completed in class

Worksheet:

Points in Three Dimensions

  • What are the directions you travel to plot the points of an ordered triple where the x, y, and z values are positive?

    • For the x, forward

    • For the y, right

    • For the z, upward


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