Tutoriel:Insérer Texte

Coordinates of Reflected Points

Preparations

• Open a new GeoGebra window.
• Show the Algebra View, Input Bar, coordinate axes and the grid (View Menu).
• In the Options Menu set the Point capturing to Fixed to Grid.

1		Create point A = (3, 1)
2		Create line a: y = 0
3		Mirror point A at line a to get point A'
4		Change the color of line a and point A'
5		Create line b: x = 0
6		Mirror point A at line b to get point A1'
7		Change the color of line b and point A1'

Inserting static text

Insert a heading into the Graphics View of GeoGebra so your students know what this dynamic figure is about:

• Activate the Text tool and click on the upper part of the Graphics View.
• Type the following text into the appearing window: Reflecting a point at the coordinate axes
• Click OK.
• Adjust the position of the text using the Move Tool.

Hint: You can change the properties of the text in the Properties Dialog (e.g. wording, font style, font size, formatting). On tab Basic you can fix the position of the text so it can’t be moved accidentally any more.

Inserting dynamic text

Dynamic text refers to existing objects and adapts automatically to modifications, for example A = (3, 1).

• Activate the Text tool and click on the Graphics View.
• Type A = into the appearing window:
  Hint: This will be the static part of the text and won’t change if point A is moved.

• Insert the dynamic part of this text by selecting point A from the Objects drop-down list.
• Click OK.

Note : The text shows the coordinates of point A and adapts automatically to modifications of its position.

Enhancing the dynamic figure

• Insert dynamic text that shows the coordinates of the reflected points A' and A1'.
• Zoom out in order to show a larger part of the coordinate plane.
  Hint: You might want to adjust the distance of the grid lines.

• • Open the Properties Dialog for the Graphics View (right click / MacOS: Ctrl - click the Graphics View and select Graphics)
  • Select tab Grid
  • Check the box next to Distance and change the values in both text fields to 1
• Close the Algebra View and fix all text so it can’t be moved accidentally.

Task

Come up with instructions to guide your students towards discovering the relation between the coordinates of the original and the reflected points which could be provided along with the dynamic figure.

Rotation of a Polygon

Preparations

• Open a new GeoGebra window.
• Hide Algebra View and Input Bar if necessary.
• Show the coordinate axes and the grid.
• Open the Properties Dialog for the Graphics View:
  • On tab xAxis change the Distance to 1
  • On tab yAxis change the Distance to 1

Construction Steps

1		Create an arbitrary triangle ABC
2		New point D at the origin of the coordinate system
3		GeoGebra offers a "fast-renaming" option. Activate Move mode and select the object. When you start typing the new name GeoGebra opens the Rename dialog window.
4		Create a slider for angle α Hint: In the slider dialog window check Angle and set the increment to 90°.
5		Rotate triangle ABC around point O by angle α Hint: Check counter clockwise rotation.
6		Segments AO and A'O
7		Angle AOA' Hint: Select the points in counter clockwise order. Hide the label of this angle.
8		Move slider and check the image of the triangle

Enhancing the Construction

1		Insert static text: Rotation of a Polygon
2		Insert dynamic text: A = and select Point A from Objects
3		Insert dynamic text: A' = and select Point A' from Objects
4		Move slider and text to desired positions
5		Fix the position of the slider (Properties Dialog – tab Slider)
6		Fix the position of the text (Properties Dialog – tab Basic)

Discussion

How could you use this file to introduce the concept of rotating an object around the origin of a coordinate system to your students?