Tutorial:Inserting Pictures into the Graphics View

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Drawing Tool for Symmetric Figures

Open 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.
Note Hint: You will learn how to create such dynamic worksheets later in this workshop.


7 symmetry.PNG
  • How could your students benefit from this prepared construction?
  • Which tools were used in order to create the dynamic figure?

Preparations

Construction Steps

1 Tool New Point.gif New point A
2 Tool Show Hide Label.gif Show the label of point A
3 Tool Line through Two Points.gif Line of reflection through two points
4 Tool Reflect Object in Line.gif Mirror point at line to get image A'
5 Tool Segment between Two Points.gif Segment between point A and its image A'
6 Trace On.gif Turn the Trace on for points A and A'
Note 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 Tool Move.gif Move point A to draw a dynamic figure

Discussion

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

Note: Make sure you have the picture A13_flower.jpg saved on your computer.
8 7 flower.PNG Insert image into the graphics view
Note Hint: Click in the lower left corner of the graphics view to insert the picture at this position.
9 Tool Move.gif Adjust the position of the inserted image.
10 Set the image as background image (Properties dialog, tab Basic).
11 Reduce the filling of the image (Properties dialog, tab Style).
Note Hint: After specifying the picture as a background image you need to open the Properties Dialog using the Edit Menu. You can’t select a background image in the Graphics View any more.


7 symmetry flower.PNG

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.

Preparations

Construction Steps

1 Insert picture A14_Sunset_Palmtrees.jpg on the left part of the Graphics View
2 Tool New Point.gif New point A at the lower left corner of the picture
3 Set point A as the first corner point of your picture.
Note 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.
Note Hint: You just changed the width of the picture to 3 cm.
6 Tool Line through Two Points.gif Vertical line through two points in the middle of the Graphics View
7 Tool Reflect Object in Line.gif Mirror the picture at the line
Note Hint: You might want to reduce the filling of the image in order to be able to better distinguish it from the original.

Tasks

  1. Move point A with the mouse. How does this affect the picture?
  2. Move the picture with the mouse and observe how this affects its image.
  3. Move the line of reflection by dragging the two points with the mouse. How does this affect the image?
7 reflect.PNG

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.

Construction Steps

1 Start with the figure you created in Resizing and Reflecting a Picture
2 Tool Delete.gif Delete the point B to restore the picture’s original size
3 Tool New Point.gif Create a new point B at the lower right corner of the original picture
4 Set the new point B as the second corner point of your picture.
Note Hint: You can now resize the image by moving point B.
5 Tool New Point.gif Create a new point E at the upper left corner of the original picture
6 Set the new point E as the fourth corner point of your picture

Tasks

  1. How does moving point E affect the picture and its image?
  2. Which geometric shape do the picture and the image form at any time?
7 disorting.PNG

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.

Construction Steps

1 Start with the figure you created in Distorting a Picture
2 Tool Segment between Two Points.gif Segment between points A and B
3 Tool Segment between Two Points.gif Segment between points A and E
4 Tool Parallel Line.gif Parallel line to segment AB through point E
5 Tool Parallel Line.gif Parallel line to segment AE through point B
6 Tool Intersect Two Objects.gif Intersect the two lines to get intersection point F
7 Tool Show Hide Object.gif Hide auxiliary objects
8 Tool Reflect Object in Line.gif Reflect all four corner points at the line to get their images
9 Tool Segment between Two Points.gif Connect corresponding points with segments (e.g. points A and A')
10 Tool Angle.gif Create angles between the line of reflection and the segments

Task

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?

7 properties reflexion.PNG
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