Getting Started: Desmos Geometry

Welcome! The Desmos Geometry Tool is a powerful and interactive workspace that allows you to visualize and explore plane geometry through construction, measurement, transformations, and more! Get started with the tips below, or check out the Geometry User Guide.

Creating Your First Construction

When you visit the Geometry tool, you’ll see the four main components: the geometry toolbar, graph paper, token navigator, and expression list.

Geometry Toolbar

The Geometry toolbar is the menu along the top containing all of the available construction tools. You can use these tools to construct points, various types of lines, circles, angles, and polygons. You can also select items with the select tool to edit or transform them.

GIF Showing the selection of different tools in the toolbar, such as the different types of lines (now including vectors), point selection, circles and angles.

 

Selected Items Menu

When you select a geometric object, the geometry toolbar changes to the Selected Items Menu. This menu allows you to delete, hide, transform, or style the selected object.

Open the transformation menu to translate, reflect, dilate, or rotate your object.

Once an object is selected, the Selected Items Menu will allow you to hide, change the color, or select an option from the transform and construct menu for your object. If you’ve selected points, segments, and/or angles, you’ll also have the option to label your object which will show the coordinate point, segment length, and/or angle measure respectively. The More Options icon, represented by three dots, will allow you to delete the selected object(s) and move an object from the token navigator to the expression list.

GIF showing a perpendicular line construction with two circles, hiding the circles, and using the more options button to move the lines into a folder in the expression list.

 

Graph Paper

The graph paper is where constructions take place. You can insert items into this space using the geometry toolbar or the expression list. Items on the graph paper are dynamic. For example, with the select tool, you can click and move draggable points and see how that movement affects the overall construction. You can also pan with the mouse and zoom with the zoom buttons.

GIF showing a perpendicular line construction, using a draggable point to enlarge the construction, then using the box select tool to drag the construction around the graph paper.

 

Token Navigator

The token navigator is at the top of the expression list (to the right of the ‘add item’ button). Here, you can see token references for the objects you construct on the graph paper. Hover over hidden tokens to reveal the location of those objects or select tokens to change the object's properties. You can also click and drag a token into the expression list to work with it algebraically, give it a name, or adjust other style settings.

GIF showing a point token and an intersection token being dragged down to the expression list.  Then, the point token being moved around the graph paper at the coordinate of the point updating in the expression list.

 

Expression List

The expression list is the panel on the left side of the screen where you can enter expressions and functions. If you’re familiar with the Desmos Graphing Calculator, you’ll notice this part is the same!

You can see a list of available functions by opening the Desmos keyboard on the bottom left. Functions specific to geometry can be found under the headings Geometry Tools, Measurements, and Transformations. In the Geometry User Guide, you will find a list of available functions, the arguments they take, and an example of each. Geometry functions can be typed into the expression list and receive inputs by selecting items on the graph paper. To input a geometric object into any function, simply shift + click on the object.

For example, let’s use the expression list to find the intersection of two circles. We can find one intersection by typing intersection() directly into the expression list, or by finding the intersection function from the keypad menu. To see both intersections, reverse the order you click on the circles.

GIF showing typing out one of the geometry functions such as intersection() and using it to show the intersection of two circles and labeling the intersection with its coordinates.  Also shows the list of Geometry tools, properties and measurements and transformation options from the function menu.

 

While many geometric functions and commands allow you to click on an object in the graph to insert it into an expression, this feature is sometimes restricted to prevent accidental inputs. However, you can insert a token wherever you’d like. To do so, place your cursor in the desired position of the expression list, then hold down shift and click on the geometry object you want to insert.

For example, the rotation function \(R(x)\) rotates an object \(x\) around the origin by \(90\) degrees. To use this rotation function, first click to place your cursor inside of the parentheses of \(R( )\), then hold shift and click on the polygon in the graph space. Give this a try by clicking on the image to open the graph.

L shape figure with a rotation function in the expression list that rotates an object x 90 degrees about the origin. There are instructions to shift+click while in the R() function to apply this rotation to the L shape.

 

Save and Share Your Construction

You can save your constructions to view and edit them later by clicking the blue ‘save’ button on the top left next to the construction title. If you press the save button while signed out, you will be prompted to sign in or create an account. You can also access all of your previously saved constructions by clicking the hamburger button on the top left.

Share your construction by clicking on the ‘share graph’ button in the top right corner next to your account name. Use this menu to copy your construction’s unique link. You can send this link to anyone, and they’ll be able to see your construction.

GIF showing the saving of a graph, name it something like “My construction”, then sharing using the Share Graph button and showing the different options: copy link, print, export and embed.

 

Learn More

Please write in with any questions or feedback to support@desmos.com.