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

## Contents

## 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

## 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 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*Basic*–*Fix object*).

### 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*.

### 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

- Open the Properties Dialog for the Graphics View (right click / MacOS: Ctrl - click the Graphics View and select
- 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]*.

*xcoordinate = x(A)*.

**Hint:**x(A) gives you the x-coordinate of point A.

*ycoordinate = y(A)*.

**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*.

### Challenge

Create a similar construction that allows for visualizing the graphical solution of a system of quadratic polynomials.**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.

Polygon | |

Angle | |

Slider | |

Midpoint | |

Rotate around Point | |

Move | |

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.**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.**Hint:**Congruent angles should have the same color.

### Challenge 1

Insert dynamic text showing that the interior angles add up to 180°.**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.

Line Through Two Points | |

Perpendicular Line | |

Intersect | |

Polygon | |

rise = y(B) - y(A) | |

run = x(B) - x(A) | |

slope = rise / run | |

Text | |

Midpoint or Center | |

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.**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)**Hint:**y(A) gives you the y-coordinate of point A.

**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.

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

### Attaching text to objects

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

- Create midpoint D of the vertical segment using tool Midpoint or center.
- Create midpoint E of the horizontal segment.
- 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*. - Select
*text2 (run = …)*in the Properties Dialog and set point E as starting point. - Hide the midpoints D and E.

## 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 | Create circle c with center A through point B. | |

3 | Zoom into the Graphics view. | |

4 | Rotate point B clockwise around point A by 120° to get point B' . | |

5 | Rotate point B clockwise around point A by 240° to get point B'1 . | |

6 | Create text1 0, text2 1 and text3 2. 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 | Create text4: New problem
| |

9 | 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 | Create text5: number = and select number from Objects.
| |

12 | Create text6: The mod 3 Clock
| |

13 | Create a slider n with an Interval from 0 to 100, Increment 1 and Width 300 (Tab Slider). | |

14 | Clockwise angle BAB'1 with given size n*120°.
| |

15 | Ray with starting point A through point B'1 . | |

16 | Create a point D = (0, 0.8). | |

17 | Create a circle d with center A through point D. | |

18 | Intersect the ray with circle d to get intersection point C. | |

19 | Hide the ray and circle d. | |

20 | Create a vector from A to C. | |

21 | Change the font size of the GeoGebra window to 20 pt. 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. |