Transformations Lab in GeoGebra

Mr. Ferraro, Balboa High School


  1. Starting GeoGebra

    Computer type/locationInstructions

    Computer Lab
    (Rm127 or Rm128)
     

    Click here to start GeoGebra. You can close the calculator at the bottom of the window.
    Chromebook
    1. Start the Chromebook.

    2. Connect to wireless network SFUSD -- username and password are the same as the ones you use for School Loop, leave all other settings alone.

    3. Create a new account:
      Username USERNAME@s.sfusd.edu, School Loop password

      Replace USERNAME with your School Loop username. For example, if my School Loop username is ferrarom, my Chromebook username will be ferrarom@s.sfusd.edu.

    4. Visit this link: Install GeoGebra Chrome App. Click the "+ free" button.

    5. Start GeoGebra by clicking here.

    6. NOTE: If you need to right-click in GeoGebra, use a two-finger tap on the touchpad!
    Room 319 Workstation/Laptop
    1. Press [ALT]+[F2]

    2. Type geogebra

    3. Press [ENTER]
     
  2. Whenever you are asked to write on your paper, make sure you include the step number.

  3. Take out a sheet of paper. Put a heading on it with your name, date, and period.

  4. Using a straightedge, draw an x-y coordinate plane on your paper.

  5. On the coordinate plane, plot these points: B(-1,3) & C(5,2). Connect the points to form segment BC.

  6. Plot a translated (i.e., shifted) version of segment BC on the same coordinate plane. Segment B'C' has these endpoints: B'(-3,6) & C'(3,5).

  7. Below your coordinate plane, write a description of the translation that produced segment B'C'.

  8. Below the description you just wrote, write down the ordered pair rule for this translation in this form:
            (x, y) ==> (?, ?)
  9. Put a new point, point A, at (1,1). You can either use the Point tool in the toolbar or type the following in the command input area at the left (or bottom) of the GeoGebra window:
            A=(1,1)
    (Note that GeoGebra requires CAPITAL letters be used for the names of points!)

  10. For a translation, GeoGebra needs a vector to describe where to shift points. Create a vector by typing this command in the command input area at the left (or bottom) of the GeoGebra window:
            vector[A]
    Again, make sure you use a capital A in that command!

  11. Using the Segment between Two Points tool, create segment BC using the same coordinates as you had on paper: B(-1,3) & C(5,2).

  12. Using the Translate Object by Vector tool (see below), click on segment BC and on the vector pointing to A. This will result in a translated version of segment BC being created.


  13. Using the Move tool (the button that looks like an arrow in the far left of the top toolbar), move point A until segment B'C' is where it was on your paper -- B'(-3,6) & C'(3,5).

  14. Write down the new location of point A on your paper and answer this question: What is the connection between point A's location and the translation rule you wrote in step #6?

  15. Now let's clear the window. Go to File -> New. (No need to save your work.)

  16. Put point A at (5, -4).

  17. Create a vector pointing to A. (See step #9.)

  18. Create segment BC such that B=(-1, 3) and C=(5, 2).

  19. Using the Translate Object by Vector tool, click on segment BC and on the vector pointing to A. This will result in a translated version of segment BC being created.

  20. On your paper, draw a new coordinate plane. Copy segments BC and B'C' to your plane.

  21. On your paper, copy the following, replacing question marks with the proper values:
            C(?, ?) ==> C'(?, ?)
    
            ordered pair rule for translation:
            (x, y) ==> (?, ?)
    

  22. Let's clear the window again. Go to File -> New. (Again, no need to save your work.)

  23. Using the Polygon tool (see below), Create a quadrilateral with these points:
            A(-1,1)
            B(2,4)
            C(8,2)
            D(7,-3)
    
    Note: To finish drawing the polygon, make sure you click on your first point again!


  24. Let's reflect quadrilateral ABCD over the y-axis. Using the Reflect Object about Line tool (see below), click on the polygon you created (click anywhere in the shaded interior) and on the y-axis. You may need to zoom out to see both figures!


  25. Write down the coordinates of B and B'.

  26. Write down the ordered pair rule that appears to be used when reflecting over the y-axis.

  27. We will now reflect quadrilateral ABCD over the line y = -4. In the command input area, type this and press [ENTER]:
            y = -4
    

  28. Using the Reflect Object about Line tool, click on quadrilateral ABCD and the line you added in the last step.

  29. Using the Move tool, drag the center of quadrilateral ABCD and notice how the two reflected images move.

  30. Complete this statement on your paper:
            As the original figure moves further from the line of reflection, 
            the reflected image ____________________________.
    

  31. Now we move on to rotations. Clear the window and re-enable automatic point capturing on the grid.

  32. Create polygon ABCDEF with these vertices:
            A(3,3)
            B(2,4)
            C(1,4)
            D(3,1)
            E(5,4)
            F(4,4)
    

  33. To rotate the figure 90° CCW, use the command input area to type this command:
            rotate[poly1,90°]
    
    Note: In order to get the degrees symbol, you can press [ALT][o] (that's the letter 'o', not the number zero!). If that doesn't work, use the degrees button (see image below).


  34. In order to rotate in the CW direction, just enter a negative number of degrees. Answer this on your paper: A rotation by how many degrees in the CW direction is equivalent to a 90° CCW rotation? If you're not sure, try this out using GeoGebra!

  35. Create a polygon of your choosing. Add the line y = x. Reflect the polygon over the line. Move your polygon around. On your paper, write the ordered pair rule for a reflection over the line y = x.

  36. Challenge: Go to Google Images and find a picture of something you like. (Choose something that is not inappropriate!) Save the image to your Desktop and insert the image into a blank GeoGebra workspace (see image below). See if you can figure out how to make your single image into the example below. Hint: Look up how to perform dilations in GeoGebra!


    Example: