[size=150][color=#1155cc]1) Using the "[b]Polygon[/b]" tool (5th button from left with a triangle on it), select "[b]Polygon[/b]" and connect the following points in order by locating each point on the (x,y) coordinate system. (Note: You will click point [b]A[/b] again after [b]D[/b] to complete the polygon.)[br][br][b] A [/b]= (2, 1), [b]B[/b] = (2, 3), [b]C[/b] = (5, 5), [b]D[/b] = (5, 1), [b]A[/b] = (2, 1)[/color][/size][br]
a. What figure did you construct?
[size=150]b) Does this figure have symmetry? How do you know?[/size]
[size=150]No, the sides will not match up if it is folded in on itself.[/size]
[size=150][color=#1155cc]2) Using the "[b]Input[/b]" line at the bottom of the applet, type the following (pressing enter after each point):[br][br] E = (-1, 1)[br] F = (1, -1)[br][br]3) Using the "[b]Line[/b]" tool (3rd button from left with a line on it), select points [b]E[/b] then [b]F[/b] to create line [b]EF[/b].[br][br]4) Select the "[b]Reflect About Line[/b]" tool (3rd button from right), and click on the center of the figure you drew in Part 1, then click on the line [b]EF[/b].[/color][br][br][/size]
[size=150]a. How did reflecting figure ABCD change the original figure? (Select ALL that apply).[/size]
[size=150]b. Compare and contrast the pre-image to the image. What do you notice?[/size]
The figure is the same except the orientation and location changed.
[size=150][color=#1155cc]5) Using the mouse, click the dropdown menu on the "[b]Line[/b]" tool (3rd button from left) and choose "[b]Segment[/b]". Using this tool, connect corresponding points to each other (A to A', B to B', C to C', and D to D').[/color][/size]
[size=150]6) What do you notice about all of the line segments? Record your observations.[/size]
All segments are parallel.
[size=150][color=#1155cc]7) Using the "[b]Input[/b]" window, create the following points (press ENTER after each point):[br][br] G = (-2, 3)[br] H = (1, 1)[br][br]8) Using the "[b]Line[/b]" tool (3rd from left), select "[b]Vector[/b]". Select points [b]G [/b]then [b]H[/b] to create vector [b]GH[/b] (Note: You must click the points in order -- [b]G[/b] then [b]H --[/b] or your vector will be pointing the wrong way.)[br][br]9) Next, use the "[b]Reflect Object About a Line[/b]" tool (3rd from right) and select "[b]Translate Object by Vector[/b]". Click on the center of the figure and then click vector [b]GH[/b].[/color][/size]
[size=150]a. What is the relationship between the vector and the two figures?[/size]
The vector shows how far and in which direction the figure will move.
[size=150]b. Using the "[b]Move[/b]" (1st button on left), drag the point [b]H[/b] around. What happens to the figure?[/size]
It moves around in the direction and distance point H is away from G.
[size=150]c. What happens when point [b]H[/b] is dragged on top of point [b]G[/b]?[/size]
The image and the pre-image are in the exact same spot.
[size=150][color=#1155cc]10) Using the "[b]Input[/b]" window, create the point [b]I[/b] = (0, 0).[br][br]11) Using the "[b]Reflect About Line[/b]" button (3rd from right), select "[b]Rotate Around Point[/b]"[br][br]12) Click the center of the figure, then point [b]I[/b]. A window should appear. Type in "angle1" (no quotation marks) for the angle, make sure counterclockwise is marked, then click OK.[/color][/size]
a. Using the "angle 1" slider, drag the point back and forth. What happens to the original figure?
Its orientation and its location change, but everything else stays the same.
[size=150]b. Rotate the object to 90˚, list the coordinates of A', B', C', and D' below.[/size]
A' = (-1, 2), B' = (-3, 2), C' = (-5, 5), D' = (-1, 5)
[size=150]c. Rotate the object to 180˚, list the coordinates of A', B', C', and D' below.[/size]
A' = (-2, -1), B' = (-2, -3), C' = (-5, -5), D' = (-5, -1)
[size=150]d. Rotate the object to 270˚, list the coordinates of A', B', C', and D' below.[/size]
A' = (1, -2), B' = (3, -2), C' = (5, -5), D' = (1, -5)
[size=150]e. Using the slider, will the two figures ever be in the same spot? Why or why not?[/size]
Yes, when the slider is at 360˚ because it has made a full rotation.
[color=#1155cc]13) Using the "[b]Point[/b]" tool (2nd from left), select "[b]Point[/b]". Plot the point [b]E[/b] at (-6, 1). (Note: You could also plot this point using the "[b]Input[/b]" line at the bottom of the applet).[br][br]14) Next, use the "[b]Line[/b]" tool (3rd from left) and select "[b]Line[/b]". Click on [b]E[/b] and [b]A[/b] to make one line [b]EA[/b], then click on [b]E[/b] then [b]C[/b] to make a second line [b]EC[/b]. (Note: Click "[b]Move[/b]" to get out of the [b]Line[/b] mode.)[br][br]15) Finally, use the "[b]Reflect Object About a Line[/b]" tool (3rd from right) and select "[b]Dilate from Point[/b]". Click on the center of your figure and then click point [b]E[/b]. A window should appear. Type in "scalefactor" (no quotation marks) for the factor, then click OK.[/color]
[size=150]a. Using the "scalefactor" slider, drag the point back and forth. What happens to the figure?[/size]
Its size, orientation, and its location change.
[size=150]b. What is the relationship between the point and the two figures (pre-image and image)? Do you notice any relationship between line segment [b]EA[/b], [b]EA'[/b], and the scale factor? What about [b]EC[/b], [b]EC'[/b], and the scale factor?[/size]
The point describes how much or little we dilate or scale our pre-image to create our image. The line segment EA' is whatever the scalefactor is times as small or as large as EA
[size=150]c. Dilate your figure by 2, then list the coordinates of A', B', C', and D' below. [/size]
A' = (10, 1), B' = (10, 5), C' = (16, 9), D' = (16, 1)
[size=150]d. Dilate your figure by 0.5, then list the coordinates of A', B', C', and D' below. [/size]
A' = (-2, 1), B' = (-2, -2), C' = (-0.5, 3), D' = (-0.5, 1)
[size=150]e. Using the slider, will the two figures ever be in the same spot? Why or why not?[/size]
Yes, when the slider is at 1 because there is no scaling up or down occurring. The dilation transformation is just replicating the same size and shape figure as before.
[size=200]✨✨✨Great job! ✨✨✨[br][br]You have finished learning how to use GeoGebra to explore ideas around transforming polygons using a dynamic geometry software. [br][br]Be sure to reflect on one thing that you learned on your guided class notes.[/size]