- 1 Drawing Tool for Symmetric Figures
- 2 Resizing and Reflecting a Picture
- 3 Distorting a Picture
- 4 Exploring Properties of Reflection
Drawing Tool for Symmetric FiguresOpen the dynamic worksheet Drawing Tool Symmetry. Follow the directions on the worksheet and experience how your students could explore the axes of symmetry of a flower.
- How could your students benefit from this prepared construction?
- Which tools were used in order to create the dynamic figure?
|1||New point A|
|2||Show the label of point A|
|3||Line of reflection through two points|
|4||Mirror point at line to get image A'|
|5||Segment between point A and its image A'|
|6||Turn the Trace on for points A and A' |
Hint: Right click (MacOS: Ctrl + click) the point and select Trace on from the menu. Whenever point A is moved it leaves a trace in the Graphics View.
|7||Move point A to draw a dynamic figure|
The Trace on feature has some special characteristics:
- The trace is a temporary phenomenon. Whenever the graphics are refreshed, the trace disappears.
- The trace can’t be saved and is not shown in the Algebra View.
- To delete the trace you need to refresh the views (menu View – Refresh Views or key combination Ctrl + F. MacOS: Open Apple + F).
Enhancing the Construction
Resizing and Reflecting a Picture
In this activity you will learn how to resize an inserted picture to a certain size and how to apply transformations to the picture in GeoGebra.
- Make sure you have the picture A14_Sunset_Palmtrees.jpg saved on your computer.
- Open a new GeoGebra window.
- Close the Algebra View and hide the coordinate axes.
|1||Insert picture A14_Sunset_Palmtrees.jpg on the left part of the Graphics View|
|2||New point A at the lower left corner of the picture|
|3||Set point A as the first corner point of your picture. |
Hint: Open the Properties Dialog and select the picture in the list of objects. Click on tab Position and select point A from the dropdown list next to Corner 1.
|4||B = A + (3, 0)|
|5||Set point B as the second corner point of the picture. |
Hint: You just changed the width of the picture to 3 cm.
|6||Vertical line through two points in the middle of the Graphics View|
|7||Mirror the picture at the line |
Hint: You might want to reduce the filling of the image in order to be able to better distinguish it from the original.
- Move point A with the mouse. How does this affect the picture?
- Move the picture with the mouse and observe how this affects its image.
- Move the line of reflection by dragging the two points with the mouse. How does this affect the image?
Distorting a Picture
In this activity you will learn how to resize an inserted picture to an arbitrary size and how to distort a picture in GeoGebra. You will now modify the construction created before. If you want to keep the original as well, you need to save your file.
- How does moving point E affect the picture and its image?
- Which geometric shape do the picture and the image form at any time?
Exploring Properties of Reflection
In this activity you will create a dynamic figure that allows your students to explore the properties of reflection. You will now modify the construction created before. If you want to keep the original as well you need to save your file.
Move the corner points of the original picture, as well as the line of reflection. What do you notice about the angles between the segments and the line of reflection? What can we call the line of reflection in relation to the segments formed by each point and its corresponding image?