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Week 12 Transformation Lab Activity

Author:
Dr. Bridget Druken, Kayla Golden
Topic:
Geometric Transformations

Part 1: Constructing the Figure

1) Using the "Polygon" tool (5th button from left with a triangle on it), select "Polygon" and connect the following points in order by locating each point on the (x,y) coordinate system. (Note: You will click point A again after D to complete the polygon.) A = (2, 1), B = (2, 3), C = (5, 5), D = (5, 1), A = (2, 1)

Questions:

a. What figure did you construct?

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

b) Does this figure have symmetry? How do you know?

Check my answer

Part 2: Reflections

2) Using the "Input" line at the bottom of the applet, type the following (pressing enter after each point): E = (-1, 1) F = (1, -1) 3) Using the "Line" tool (3rd button from left with a line on it), select points E then F to create line EF. 4) Select the "Reflect About Line" tool (3rd button from right), and click on the center of the figure you drew in Part 1, then click on the line EF.

Questions:

a. How did reflecting figure ABCD change the original figure? (Select ALL that apply).

Select all that apply
  • A
  • B
  • C
  • D
Check my answer (3)

b. Compare and contrast the pre-image to the image. What do you notice?

Check my answer
5) Using the mouse, click the dropdown menu on the "Line" tool (3rd button from left) and choose "Segment". Using this tool, connect corresponding points to each other (A to A', B to B', C to C', and D to D').

6) What do you notice about all of the line segments? Record your observations.

Check my answer

Part 3: Translations

7) Using the "Input" window, create the following points (press ENTER after each point): G = (-2, 3) H = (1, 1) 8) Using the "Line" tool (3rd from left), select "Vector". Select points G then H to create vector GH (Note: You must click the points in order -- G then H -- or your vector will be pointing the wrong way.) 9) Next, use the "Reflect Object About a Line" tool (3rd from right) and select "Translate Object by Vector". Click on the center of the figure and then click vector GH.

Questions:

a. What is the relationship between the vector and the two figures?

Check my answer

b. Using the "Move" (1st button on left), drag the point H around. What happens to the figure?

Check my answer

c. What happens when point H is dragged on top of point G?

Check my answer

Part 4: Rotations

10) Using the "Input" window, create the point I = (0, 0). 11) Using the "Reflect About Line" button (3rd from right), select "Rotate Around Point" 12) Click the center of the figure, then point I. A window should appear. Type in "angle1" (no quotation marks) for the angle, make sure counterclockwise is marked, then click OK.

Questions:

a. Using the "angle 1" slider, drag the point back and forth. What happens to the original figure?

Check my answer

b. Rotate the object to 90˚, list the coordinates of A', B', C', and D' below.

Check my answer

c. Rotate the object to 180˚, list the coordinates of A', B', C', and D' below.

Check my answer

d. Rotate the object to 270˚, list the coordinates of A', B', C', and D' below.

Check my answer

e. Using the slider, will the two figures ever be in the same spot? Why or why not?

Check my answer

Part 5: Dilations

13) Using the "Point" tool (2nd from left), select "Point". Plot the point E at (-6, 1). (Note: You could also plot this point using the "Input" line at the bottom of the applet). 14) Next, use the "Line" tool (3rd from left) and select "Line". Click on E and A to make one line EA, then click on E then C to make a second line EC. (Note: Click "Move" to get out of the Line mode.) 15) Finally, use the "Reflect Object About a Line" tool (3rd from right) and select "Dilate from Point". Click on the center of your figure and then click point E. A window should appear. Type in "scalefactor" (no quotation marks) for the factor, then click OK.

Questions:

a. Using the "scalefactor" slider, drag the point back and forth. What happens to the figure?

Check my answer

b. What is the relationship between the point and the two figures (pre-image and image)? Do you notice any relationship between line segment EA, EA', and the scale factor? What about EC, EC', and the scale factor?

Check my answer

c. Dilate your figure by 2, then list the coordinates of A', B', C', and D' below.

Check my answer

d. Dilate your figure by 0.5, then list the coordinates of A', B', C', and D' below.

Check my answer

e. Using the slider, will the two figures ever be in the same spot? Why or why not?

Check my answer
✨✨✨Great job! ✨✨✨ You have finished learning how to use GeoGebra to explore ideas around transforming polygons using a dynamic geometry software. Be sure to reflect on one thing that you learned on your guided class notes.

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