Tutorial:Inserting Static and Dynamic Text into the GeoGebra’s Graphics View

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Coordinates of Reflected Points

Preparations

  • Open a new GeoGebra window.
  • Switch to Perspectives - Algebra & Graphics and show the grid (View Menu).
  • In the Options Menu set the Point capturing to Fixed to Grid.

Construction Steps

1 Tool New Point.gif Create point A = (3, 1)
2 Create line a: y = 0
3 Tool Reflect Object in Line.gif Mirror point A at line a to get point A'
Note Hint: You might want to match the color of line a and point A'
4 Create line b: x = 0
5 Tool Reflect Object in Line.gif Mirror point A at line b to get point A1'
Note Hint: You might want to match the color of line b and point A1'

Inserting Text into the Graphics View

Inserting static text

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

  • Activate the Tool Insert Text.gif 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.
  • Fix the position of the text so it can’t be moved accidentally (Properties dialog – tab BasicFix object).

Inserting dynamic text

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

  • Activate the Tool Insert Text.gif Text tool and click on the Graphics View.
  • Type A = into the appearing window:
    Note 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.

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.
    Note 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.

Visualizing a System of Linear Equations

Preparations

  • Open a new GeoGebra window.
  • Switch to Perspectives – Algebra & Graphics and show the grid (View Menu).

Construction Steps

1. Create sliders m_1 and b_1 using the default settings for sliders.

2. Create the linear equation l_1: y = m_1 x + b_1.

3. Create sliders m_2 and b_2 using the default settings for sliders.

4. Create the linear equation l_2: y = m_2 x + b_2.

5. Create dynamic text1: Line 1: and select l_1 from Objects.

6. Create dynamic text2: Line 2: and select l_2 from Objects.

7. Construct the intersection point A of both lines either using Tool Intersect or command A = Intersect[l_1, l_2].

8. Define xcoordinate = x(A).
Note Hint: x(A) gives you the x-coordinate of point A.
9. Define ycoordinate = y(A).
Note Hint: y(A) gives you the y-coordinate of point A.

10. Create dynamic text3: Solution: x = and select xcoordinate from Objects. Type in y = and select ycoordinate from Objects.

9 equations.PNG

Challenge

Create a similar construction that allows for visualizing the graphical solution of a system of quadratic polynomials.
Note Hint: Functions need to be entered using the syntax f(x) = …
Note: Such a dynamic figure can also be used to visualize an equation in one variable by entering each side of the equation as one of the two functions.

Visualizing the Angle Sum in a Triangle

In this activity you are going to use the following tools. Make sure you know how to use each tool before you begin.

Tool Polygon.gif Polygon
Tool Angle.gif Angle
Tool Slider.gif Slider
Tool Midpoint or Center.gif Midpoint
Tool Rotate Object around Point by Angle.gif Rotate around Point
Tool Move.gif Move
Tool Insert Text.gif Insert Text

Preparations

  • Open a new GeoGebra window.
  • Switch to Perspectives – Geometry.
  • Show the input bar (View Menu).
  • Set the number of decimal places to 0 (menu Options – Rounding).

Construction Steps

1. Create a triangle ABC.
Note Hint: Use counterclockwise orientation.

2. Create the angles α, β, and γ of triangle ABC.

3. Set the number of decimal places to 0 (Options Menu).

4. Create sliders δ and ε with the settings angle (type); 0° to 180° (interval); 10° (increment).

5. Create midpoint D of segment AC and midpoint E of segment AB.

6. Rotate the triangle around point D by angle δ (setting clockwise).

7. Rotate the triangle around point E by angle ε (setting counterclockwise).

8. Move both sliders to show 180° before you create the angles ζ (A’C’B’) and η (C'1B'1A'1).

9. Enhance your construction using the Properties Dialog.
Note Hint: Congruent angles should have the same color.


13 anglesum.PNG

Challenge 1

Insert dynamic text showing that the interior angles add up to 180°.
Note Hint: reate dynamic text for the interior angles (e.g. α = and select α from Objects), calculate the angle sum using sum = α + β + γ and insert the sum as a dynamic text.

Match colors of corresponding angles and text. Fix the text in the Graphics View.

Challenge 2

Export the figure to a dynamic worksheet. Come up with instructions that guide your students towards discovering the angle sum in a triangle. Have them check their conjecture using the provided worksheet.

Constructing a Slope Triangle

In this activity you are going to use the following tools and algebraic input. Make sure you know how to use each tool and the syntax for algebraic input before you begin.

Tool Line through Two Points.gif Line Through Two Points
Tool Perpendicular Line.gif Perpendicular Line
Tool Intersect Two Objects.gif Intersect
Tool Polygon.gif Polygon
rise = y(B) - y(A)
run = x(B) - x(A)
slope = rise / run
Tool Insert Text.gif Text
Tool Midpoint or Center.gif Midpoint or Center
Tool Move.gif Move

Preparations

  • Open a new GeoGebra window.
  • Switch to Perspectives – Algebra & Graphics and show the grid (View Menu).
  • Set the point capturing to Fixed to Grid (menu Options – Point capturing).
  • Set the labeling to All New Objects (menu Options – Labeling).

Construction Steps

1. Create line a through two points A and B.

2. Construct a perpendicular line b to the y-axis through point A.

3. Construct a perpendicular line c to the x-axis through point B.

4. Intersect perpendicular lines b and c to get intersection point C.
Note Hint: You might want to hide the perpendicular lines.

5. Create polygon ACB.

6. Hide the labels of the triangle sides.

7. Calculate the rise: rise = y(B) - y(A)
Note Hint: y(A) gives you the y-coordinate of point A.
8. Calculate the run: run = x(B) - x(A)
Note Hint: x(B) gives you the x-coordinate of point B.

9. Insert dynamic text: rise = and select rise from Objects.

10. Insert dynamic text2: run = and select run from Objects.

11. Enter the following equation into the input bar to calculate the slope of line a: slope = rise / run

12. Insert dynamic text3: slope = and select slope from Objects.

13. Change properties of objects in order to enhance your construction and fix text that is not supposed to be moved.

Dynamic Fractions and Attaching Text to Objects

Inserting dynamic fractions

Using LaTeX formulas, text can be enhanced to display fractions, square roots, or other mathematical symbols.

  1. Activate tool Insert text and click on the Graphics View.
  2. Type slope = into the Insert text window’s input bar.
  3. Check LaTeX formula and select Roots and Fractions a/b from the dropdown list.
  4. Place the cursor within the first set of curly braces and replace a by number rise from the Objects drop-down list.
  5. Place the cursor within the second set of curly braces and replace b by number run from the Objects drop-down list.
  6. Click OK.

Attaching text to objects

Whenever an object changes its position, attached text adapts to the movement and follows along.

  1. Create midpoint D of the vertical segment using tool Midpoint or center.
  2. Create midpoint E of the horizontal segment.
  3. Open the Properties Dialog and select text1 (rise = …). Click on tab Position and select point D from the drop-down list next to Starting point.
  4. Select text2 (run = …) in the Properties Dialog and set point E as starting point.
  5. Hide the midpoints D and E.
9 slope.PNG

The mod 3 Clock

The mod 3 clock allows you to determine the remainder if you divide a given number by 3. In this dynamic figure you can create a random number between 0 and 100. Moving the blue slider causes the hand of the clock to rotate. When the value of the slider matches the given number, the hand of the clock points at the corresponding remainder for division by 3.

Preparations

  • Open a new GeoGebra window.
  • Switch to Perspectives – Algebra & Graphics.

Construction Steps

1 Create points A = (0, 0) and B = (0, 1).
2 Tool Circle Center Point.gif Create circle c with center A through point B.
3 Tool Zoom In.gif Zoom into the Graphics view.
4 Tool Rotate Object around Point by Angle.gif Rotate point B clockwise around point A by 120° to get point B' .
5 Tool Rotate Object around Point by Angle.gif Rotate point B clockwise around point A by 240° to get point B'1 .
6 Tool Insert Text.gif Create text1 0, text2 1 and text3 2.
Note Hint: You might want to edit the text (bold, large font size).
7 Attach text1 to point B, text2 to point B' and text3 to point B'1 (Properties Dialog).
8 Tool Insert Text.gif Create text4: New problem
9 Tool Slider.gif Create a slider a with an Interval from 0 to 100 and Increment 1.
10 Create a random number between 0 and 100: number = floor(100 * random()) + a - a {{note: Function random() gives you a random number between 0 and 1. If you multiply this random number by 100 you get a decimal between 0 and 100. Function floor() gives you the greatest integer less or equal to the decimal, thus, an integer between 0 and 100. The extension + a - a allows you to create a new problem whenever the slider is moved.}}
11 Tool Insert Text.gif Create text5: number = and select number from Objects.
12 Tool Insert Text.gif Create text6: The mod 3 Clock
13 Tool Slider.gif Create a slider n with an Interval from 0 to 100, Increment 1 and Width 300 (Tab Slider).
14 Tool Angle Fixed.gif Clockwise angle BAB'1 with given size n*120°.
15 Tool Ray through Two Points.gif Ray with starting point A through point B'1 .
16 Create a point D = (0, 0.8).
17 Tool Circle Center Point.gif Create a circle d with center A through point D.
18 Tool Intersect Two Objects.gif Intersect the ray with circle d to get intersection point C.
19 Tool Show Hide Object.gif Hide the ray and circle d.
20 Tool Vector between Two Points.gif Create a vector from A to C.
21 Change the font size of the GeoGebra window to 20 pt.
Note Hint: Menu Options – Font size
22 Use the Properties dialog to enhance your construction and fix text and sliders so they can’t be moved accidentally.
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