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GeoGebra

Transformation Lab Activity

作成者:Julie Ryle, Kayla Golden
トピック:移動・変換

Part 1: Constructing the Figure

1) Using the "Polygon" tool (5th button from right), select polygon and connect the following points in order by clicking on each point. (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?

該当するものを全て選択
  • A
  • B
  • C
  • D
答 (3)を確認

b) Does this figure have symmetry?

該当するものを全て選択
  • A
  • B
答 (3)を確認

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), 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).

該当するものを全て選択
  • A
  • B
  • C
  • D
答 (3)を確認

b. Is this an isometry?

該当するものを全て選択
  • A
  • B
答 (3)を確認
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.

答えを確認

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. How did translating figure change the original figure? (Select ALL that apply).

該当するものを全て選択
  • A
  • B
  • C
  • D
答 (3)を確認

b. Is this an isometry?

該当するものを全て選択
  • A
  • B
答 (3)を確認
Using the "Move" (1st button on left), drag the point H around. Notice what happens to the figure if point H is dragged on top of point G.

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?

該当するものを全て選択
  • A
  • B
  • C
  • D
答 (3)を確認

b. Is this an isometry?

該当するものを全て選択
  • A
  • B
答 (3)を確認

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

答えを確認

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

答えを確認

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

答えを確認

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

答えを確認

Part 5: Dilations

13) Using the "Input" window, create the following point (press ENTER after each point): J = (9, 1) 14) Using the "Reflect About Line" button (3rd from right), select "Dilate from a Point". Click on the center of the figure and then click point J. Then, enter the factor 2.

Questions:

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

該当するものを全て選択
  • A
  • B
  • C
  • D
答 (3)を確認

b. Is this an isometry?

該当するものを全て選択
  • A
  • B
答 (3)を確認

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