In this section, you will learn how to use the Tools View in the GeoGebra Graphing Calculator. Tools allow you to create and analyze mathematical objects by selecting buttons and clicking directly in the Graphics View rather than typing commands.

This tutorial uses the individual GeoGebra Graphing Calculator. The Calculator Suite and Geometry app contain additional construction tools, so the available options may look different if you open another GeoGebra app.

By the end of this section, you will be able to:

• Open and navigate the Tools View

• Select and use a GeoGebra tool

• Create and move points

• Create lines, rays, and vectors

• Find roots, extrema, and intersections

• Create and adjust a slider

• Add text to the Graphics View

• Move and zoom the coordinate plane

• Select, hide, show, and delete objects

Step 1: Open the Graphing Calculator

1. Go to the GeoGebra website.

2. Open the Graphing Calculator.

3. Locate the tabs or buttons for:

   • Algebra

   • Tools

   • Table

4. Select Tools.

The Tools View provides buttons for creating points, lines, vectors, sliders, and other objects. It also contains tools for analyzing functions and managing the Graphics View.

Step 2: Explore the Tools View

The tools are organized into categories. Depending on your device and screen size, you may see categories such as:

• Basic Tools

• Edit

• Media

• Points

• Lines

• Others

Select a category to see the tools available within it.

Some tools may appear in more than one category. For example, the Point and Intersect tools may appear under both Basic Tools and Points.

Step 3: Learn How Tools Work

Most GeoGebra tools follow the same process:

1. Select a tool.

2. Read the instructions that appear for the tool.

3. Select the required objects or locations in the Graphics View.

4. Complete the construction.

5. Return to the Move tool when you are finished.

The order in which you select objects may be important. For example, a line requires two points, while an intersection requires two objects. GeoGebra displays a tooltip or instruction explaining what must be selected.

Step 4: Use the Move Tool

The Move tool allows you to select and move objects.

1. Open Basic Tools.

2. Select Move.

3. Select an existing point.

4. Drag the point to a new location.

5. Observe how its coordinates change in the Algebra View.

Only free objects can be moved freely. An object that depends on another object may be limited in how it can move. When the Move tool is active, you can also select an object and use the arrow keys to adjust its position.

Step 5: Create a Point

The Point tool creates a point anywhere in the Graphics View.

1. Open the Points category.

2. Select Point.

3. Click anywhere in the Graphics View.

4. Click a second location to create another point.

5. Return to the Move tool.

GeoGebra assigns capital-letter names such as A, B, and C to points. The coordinates of each point are displayed in the Algebra View.

Practice

Create two points:

• Point A in Quadrant I

• Point B in Quadrant II

Use the Move tool to change the location of each point.

Step 6: Create a Point on an Object

The Point on Object tool attaches a point to an existing graph or object.

1. Enter the following function in the Algebra View:

f(x) = x^2

2. Return to the Tools View.

3. Open the Points category.

4. Select Point on Object.

5. Click directly on the graph of f.

6. Select the Move tool.

7. Drag the new point along the graph.

The point remains attached to the function and can only move along the graph.

Step 7: Create a Line

The Line tool creates a line through two points.

1. Make sure points AAA and BBB are visible.

2. Open the Lines category.

3. Select Line.

4. Select point AAA.

5. Select point BBB.

GeoGebra creates a line that passes through both points. You can also create a line by selecting the Line tool and clicking two empty locations in the Graphics View.

Select the Move tool and drag point A or B. Observe how the line updates automatically..

Step 8: Create a Ray

A ray has one endpoint and continues indefinitely in one direction.

1. Open the Lines category.

2. Select Ray.

3. Select point A first.

4. Select point B second.

The first point becomes the endpoint of the ray. The second point determines its direction.

Create another ray by reversing the order:

1. Select point B.

2. Select point A.

Compare the two rays.

Step 9: Create a Vector

A vector represents both magnitude and direction.

1. Open the Lines category.

2. Select Vector.

3. Select point a as the initial point.

4. Select point b as the terminal point.

GeoGebra creates a vector pointing from a to b.

Now create a second vector from b to a. Observe how reversing the order changes the direction of the vector.

Step 10: Use the Intersect Tool

The Intersect tool identifies where two mathematical objects meet.

First, enter these functions:

f(x) = x^2 - 4

g(x) = x

Then:

1. Open Basic Tools or the Points category.

2. Select Intersect.

3. Select the graph of fff.

4. Select the graph of ggg.

GeoGebra creates points at each intersection. You may also click directly on one visible intersection to create only that point.

Step 11: Use the Roots Tool

The Roots tool identifies the zeros of a function. These are the points where the function crosses or touches the xxx-axis.

Using the function

f(x) = x^2 - 4

complete the following:

1. Open Basic Tools or the Points category.

2. Select Roots.

3. Select the graph of fff.

GeoGebra creates points at the roots of the function.

For this example, the roots are located at x=−2x=-2x=−2 and x=2x=2x=2.

Step 12: Use the Extremum Tool

The Extremum tool identifies the maximum or minimum points of a function.

1. Select Extremum from the Tools View.

2. Select the graph of:

f(x) = x^2 - 4

GeoGebra identifies the minimum point of the parabola.

The point appears in both the Algebra View and the Graphics View.

Step 13: Create a Slider

A slider allows you to change the value of a number dynamically.

1. Open Basic Tools.

2. Select Slider.

3. Click an empty location in the Graphics View.

4. Enter the following settings:

   • Name: a

   • Minimum: -5

   • Maximum: 5

   • Increment: 0.5

5. Create the slider.

The Slider tool allows you to specify the variable’s name, minimum value, maximum value, and increment.

Now enter:

h(x) = a * x + 1

Move the slider and observe how the graph changes as the value of aaa changes.

Step 14: Add Text

The Text tool allows you to add a title, label, or instruction to the Graphics View.

1. Open the Media category.

2. Select Text.

3. Click where you want the text to appear.

4. Enter:

My GeoGebra Construction

5. Confirm the text.

6. Use the Move tool to reposition it.

Text can be used to add directions or explanations to a construction. Text is one of GeoGebra’s action and media object tools.

Step 15: Select and Format an Object

To change the appearance of an object:

1. Select the Move or Select Objects tool.

2. Select a point, line, function, or other object.

3. Open the object’s style or settings menu.

4. Change one or more of the following:

   • Color

   • Line thickness

   • Line style

   • Point size

   • Point style

   • Label visibility

5. Close the settings menu.

Formatting can make a construction easier to read and can help distinguish between different mathematical objects.

Step 16: Hide and Show an Object

Hiding an object removes it from the Graphics View without deleting it.

1. Locate an object in the Algebra View.

2. Select the visibility icon next to the object.

3. Observe that the object disappears from the Graphics View.

4. Select the visibility icon again to show the object.

A hidden object remains part of the construction. Any objects that depend on it will continue to work.

Step 17: Move the Graphics View

The Move Graphics View tool changes which part of the coordinate plane is visible.

1. Open the Edit category.

2. Select Move Graphics View.

3. Click and drag the background of the coordinate plane.

4. Move the coordinate plane left, right, up, and down.

This moves the view rather than moving the mathematical objects.

Step 18: Zoom In and Out

You can adjust the scale of the coordinate plane by:

• Using the mouse scroll wheel

• Pinching on a touchscreen

• Selecting the Zoom In or Zoom Out tools when available

• Using the zoom controls in the Graphics View

Zooming changes how much of the coordinate plane is visible. It does not change the mathematical definitions of the objects.

Step 19: Delete and Undo

To delete an object:

1. Select the object.

2. Open its menu.

3. Select Delete.

You can also select an object and press the Delete or Backspace key.

To restore an object that was deleted accidentally, select Undo or use:

• Ctrl + Z on Windows

• Command + Z on a Mac

GeoGebra supports keyboard controls for deleting selected objects, undoing actions, and navigating between objects.

Tools Practice

Open a blank GeoGebra Graphing Calculator and complete the following construction:

1. Use the Point tool to create points A and B.

2. Use the Line tool to create a line through A and B.

3. Use the Vector tool to create a vector from A to B.

4. Enter:

f(x) = x^2 - 4

5. Enter:

g(x) = x

6. Use the Roots tool to identify the roots of f.

7. Use the Extremum tool to identify the minimum of f.

8. Use the Intersect tool to find the intersections of f and g.

9. Create a slider named a.

10. Enter:

h(x) = a * x + 1

11. Move the slider and observe the graph.

12. Change the color or style of one object.

13. Hide one function.

14. Move the coordinate plane.

15. Delete one object and use Undo to restore it.