Welcome to the Desmos Geometry Tool
You can use the Desmos Geometry Tool for constructions and transformations, to explore geometric relationships and measurements, and much more. You can do all of this dynamically because the Graphing Calculator is built into the tool.
If you have questions that aren’t answered here, please visit help.desmos.com or send us an email at support@desmos.com.
Construction Tools, Settings, and Key Features
When you visit the Geometry Tool, you’ll find an expression list, blank graph paper, and a toolbar. You can use both the toolbar and the expression list to add objects to the graph paper. Once you add objects, you can click the Token Navigator to find references to all of them.
Use the Construction Tools
Access each construction tool by finding and clicking them in the toolbar. To navigate the toolbar with a keyboard, type Ctrl+Alt+M (Windows) or Ctrl+Cmd+M (Mac).
Select
Click Select Tool to select individual objects on the graph paper. To select multiple objects, hold Shift as you select. Or, click the Select Tool dropdown and then choose Box Select.
Point Objects
Select Point Objects to add a point by clicking directly on the graph paper. You can also add a point by typing its coordinates into an expression line.
Select the Point Objects dropdown and then Midpoint to find the midpoint of a segment or two points you have selected from the graph paper. Or, you can type the function midpoint( ) in an expression line.
Line Objects
Select the Line Objects dropdown to find options for creating segments, lines, rays, and vectors; creating a parallel or perpendicular line to an object on the graph paper; or adding an angle bisector to an angle on the graph paper.
To create a segment, line, or ray, choose your preference from the Line Objects dropdown. Then, click two new or existing points on the graph paper to connect them.
You can use the Vector option in two ways. The first is to create a vector independent of other objects. Select Vector from the Line Objects dropdown. Then, click on a new or existing start and end point on the graph paper. After that, you can click an existing vector to make a copy and then place that copy at a new starting point.
The second is to create a vector parallel or perpendicular to an existing line. Choose your preference from the Line Objects dropdown. Then, select an existing line on the graph paper. This will create a parallel or perpendicular line. Click anywhere on the graph paper to place the new line.
Use the Angle Bisector option to create a ray that bisects any angle you select on the graph paper.
The functions segment( ), line( ), ray( ), vector( ), parallel( ), perpendicular( ), and anglebisector( ) can also produce the same results.
Circle Objects
To add a circle to your graph, first click the Circle Objects dropdown. Then, click one new or existing point on the graph paper to set the center of your circle. Next, click another new or existing point to set the circumference. Or, you can type the function circle( ) in the expression list.
To create a circle with the compass, click the Circle Objects dropdown and then select Circle by Length. Click an existing segment on your graph paper to determine the length of the radius. Then, click anywhere on the graph paper to place the center of your circle.
To create an arc with the compass, select Arc instead. Click three new or existing points on the graph paper to place the arc. Or, type the function arc( ) in an expression line.
Angle Objects
Click Angle Objects to create and label the measure of an angle. First, select three points on the graph paper to define the angle. Then, click any three new or existing points on the graph paper to define the angle.
To measure the angle of a polygon, choose your angle type from the dropdown menu and then click an existing polygon on the graph paper. Doing so will label all interior angles of the polygon.
Polygon Objects
Click Polygon Objects to create a polygon. On the graph paper, click to create points. These will be the vertices of the polygon. Or, type the function polygon( ) in an expression line.
Learn more about the polygon function in our Help Center.
Navigate the Graph With a Keyboard
To navigate the graph paper with a keyboard, press Ctrl+Alt+P (Windows) or Ctrl+Cmd+P (Mac) to focus the graph paper. Press Tab to move through geometry objects on the graph paper, and use arrow keys to navigate. Press Enter (Windows), Return (Mac), or Spacebar to click or choose an object or location.
Accessibility: With a screen reader, your position on the graph paper is reported in either math coordinates (if the axes are on) or in percentages from the top and left of the screen.
Geometry tool hints are spoken aloud automatically when you activate a new tool or when the input for the selected tool has updated. Alerts are also spoken when you add new geometry objects to the canvas.
Adjust the Geometry Settings
Click Geometry Settings or type Ctrl+Alt+G (Windows) or Ctrl+Cmd+G (Mac) to open the menu. From the menu, you can show or hide the grid and axes, switch between using radians and degrees for angles, and more. If you’ve hidden a geometry object, you'll also see a checkbox in this menu that you can use to reveal the location of those hidden objects.
Construct After Selecting an Object
When you select an object from the graph paper or a token from the navigator, the Selected Objects menu will appear where the geometry toolbar was. From this menu, you can change the properties of an object. You can also transform or construct from the object(s) that have been selected.
Depending on the object(s) you have selected, you will see different construction options in this menu. As an example, try selecting a segment. From a selected segment, you can add its midpoint, construct parallel or perpendicular lines to it, or use it as the length by which to define the radius of a circle. You can also transform the selected segment. Read more about transformations later in this guide.
Construct From the Expression List
When you work in the expression list, you can click on objects on the graph paper to use a token reference to the object in your expression.
To insert a token anywhere into an expression, place your cursor at the desired position. Then, hold down Shift and then click any geometry object you want to include. In some expressions, this ability is limited to avoid unintentional inputs.
Explore With the Token Navigator
Click Token Navigator to see token references for the objects you construct on the graph paper. Select a token to emphasize its object on the graph paper. Or, click an object on the graph paper to emphasize its token.
Hidden tokens will appear as grayscale icons. Hover over hidden tokens to reveal the location of those objects on the graph paper. You can also click and drag a token into the expression list to work with it algebraically or give it a name.
Save and Share Your Graph
Create an Account
You can use the Desmos Geometry Tool without logging in, but you must log in to save your graphs. If you press Save while signed out, you will be prompted to sign in or create an account. If you already have a Desmos account from using the Graphing Calculator or another tool, you can use the same one to log in to the Geometry Tool.
Otherwise, select Sign Up to make an account with an email address or by signing up with Google or Apple.
Save Your Graph
Each time you make changes to your graph, the Save button will turn blue. To save any updates or changes, click Save or type Ctrl+S (Windows) or Cmd+S (Mac). If you’ve previously saved the graph you are working on, you can select the More Options dropdown menu to rename or duplicate your graph.
Access Your Saved Graphs
To access all of your saved graphs, click Open File or type Ctrl+O (Windows) or Cmd+O (Mac). To open any of your saved graphs, click the file’s thumbnail. Or, use your arrow keys to find the thumbnail and then press Enter to open your graph.
Share Your Graph
Click Share Graph or type Ctrl+Alt+S (Windows) or Ctrl+Cmd+S (Mac) to share or export your graph. Select Share a Snapshot to create a link to the current version of your graph. People with access to this link won’t see any changes you make to your original graph. Or, you can select Save and Share This Graph to create a link that updates as you save changes to your graph.
Organize Your Saved Graphs
You can organize your graphs by grouping them within folders. To create a new folder, first click Open File . Then, click the New Geometry dropdown and select New Folder.
To add a file or multiple files to a folder, check the box on each file’s thumbnail. Then, drag them into the desired folder or select Move Items to place them into the folder.
Quick Tip: If you forget to save your graph, you can attempt to recover it. Select Open File and click or tab to select Lost Work? Attempt Recovery. You need to be signed in to attempt a recovery of lost work.
Gallery View
Once you have a folder, click the folder options dropdown and select Open Gallery View. The gallery will open in a separate tab. Select Share This Gallery to get a link to send the collection to others.
Object Properties, Labels, and Measurements
You can measure, label, and style geometry objects from the toolbar or from the expression list.
Select an Object and Edit Its Properties
When you select an object, the toolbar becomes the Selected Objects menu. It includes options to hide, change the color, label, or transform or construct from the object(s) you have selected. Open the More Options menu to delete, turn on draggable points, or move the object(s) to the expression list.
Change the Color or Properties of an Object
To explore all of an object’s style options, open the Style menu by dragging the object’s token to the expression list and then pressing and holding the object’s Color Icon . Depending on the item, you can change the opacity, color, location of the label, and other style options.
Label Points and Angles
Go to the Selected Objects menu and then click Label to label points and angles. Points default to letter labels, and angles default to their measurement. If the axes are turned on, you will also have the option to label the point with its coordinates.
Label Length
You can also label the length of a segment. Click the Label dropdown and then Length. On the graph paper, segments are labeled with a length rounded to the nearest hundredth of a unit. You can also measure the length of a segment by typing length( ) into the expression list.
Other Measurements
The distance function finds the distance between two points. You can also find the perimeter and area of polygons and the radius of a circle. To use any of these functions, click Show Keypad and then Functions. Then, scroll to the Properties & Measurements section to view more functions.
Operations With Angle Measurements
In the expression list, you can operate with the measurements of geometric objects. Angles are unique because you do not need a separate function to compute with their measurement. Instead, you can use their angle token in the expression list. You can click the angle object on the graph paper to add its reference token to an expression line.
Operations With Vectors
Like angles, you can use a vector token to compute with a vector in the expression list. Click the vector on the graph paper to add its reference token to an expression line. You can add and subtract vectors or use them in scalar multiplication.
Transformations
You can translate, reflect, dilate, and rotate any geometry object on the graph paper.
Use a Transformation Tool
Select a geometry object and then click the Transform and Construct menu. From there, you will see four transformation options. Depending on the object you select, you might also see construction options.
| Transformation | Arguments |
|---|---|
| Translate | Start point and end point or a vector object |
| Reflect | Line, segment, or ray to reflect across |
| Dilate | Center point for dilation and a scale number |
| Rotate | Center point for rotation and a directed angle |
A transformation will create a new object on the graph paper. The new object is dependent on the first object, and you can edit or transform the new object further. This means that you can apply multiple transformations in sequence.
Open the Transform and Construct menu and find the Recent Transformations section to view and track the transformations you’ve applied to the object.
Use Sliders and Lists
When you dilate or rotate an object, you can enter numerical inputs for the scale factor or rotation angle. You can also use a slider or list from the expression list to show how a transformation progresses as its inputs change.
Transformations as Functions
Click the Token Navigator to find references to defined transformations along with your objects. From there, you can drag the transformation into the expression list to see it defined in function notation. For example:
\(T\)\((x)=\) rotate\((x\), , \(90)\)
You can then apply transformation functions to other geometry objects. You can also apply a transformation to an object in one line without defining it separately as a function.
Geometry Functions
Geometry Tools
| Function | Try typing... | Arguments | This function plots a... |
|---|---|---|---|
| midpoint | midpoint\(\mathbf{\Bigl(}\) |
segment or two points | point equidistant from two endpoints of a segment or between two points |
| intersection | intersection\(\mathbf{\Bigl(}\) |
two intersecting lines, circles, or arcs | common point between two objects |
| segment | segment\(\mathbf{\Bigl(}\) |
two points | part of a line with two endpoints |
| line | line\(\mathbf{\Bigl(}\) |
two points | collection of points in a straight path |
| ray | ray\(\mathbf{\Bigl(}\) |
two points | part of a line with only one endpoint |
| parallel | parallel\(\mathbf{\Bigl(}\) |
line object and a point | line that does not intersect in the same plane |
| perpendicular | perpendicular\(\mathbf{\Bigl(}\) |
line object and a point | linee that intersects in a plane at a right angle |
| angle bisector | anglebisector\(\mathbf{\Bigl(}\) |
angle | ray that splits an angle into two congruent angles |
| circle | circle\(\mathbf{\Bigl(}\) |
center point and another point, segment, or number | collection of points equidistant from a center |
| arc | arc\(\mathbf{\Bigl(}\) |
three points | curved path through three points on the same circle |
| angle | angle\(\mathbf{\Bigl(}\) |
three points | amount of rotation from one line to the other about a common vertex |
| directed angle | directedangle\(\mathbf{\Bigl(}\) |
three points | measured angle (positive counter-clockwise and negative clockwise) |
| polygon | polygon\(\mathbf{\Bigl(}\) |
n points | closed plane figure made of points and segments |
| glider | glider\(\mathbf{\Bigl(}\) |
object, then a number—usually between 0 and 1 from the start to the end | point restricted to another object that follows that object’s path |
| vector | vector\(\mathbf{\Bigl(}\) |
start point and end point | marker that shows both a direction and a magnitude |
Properties & Measurements
| Function | Try typing... | Arguments | This function finds the... |
|---|---|---|---|
| length | length\(\mathbf{\Bigl(}\) |
segment | measure of a segment |
| distance | distance\(\mathbf{\Bigl(}\) |
two points | measure between two points |
| area | area\(\mathbf{\Bigl(}\) |
polygon | measure of space contained by a polygon |
| perimeter | perimeter\(\mathbf{\Bigl(}\) |
polygon | total length of all segments of a polygon |
| vertices | vertices\(\mathbf{\Bigl(}\) |
polygon | intersection points of the segments of a polygon |
| angles | angles\(\mathbf{\Bigl(}\) |
polygon | measured rotations for each pair of adjacent segments in a polygon |
| directed angles | directedangles\(\mathbf{\Bigl(}\) |
polygon | angles measured with direction in a polygon |
| segments | segments\(\mathbf{\Bigl(}\) |
polygon | edges of a polygon |
| radius | radius\(\mathbf{\Bigl(}\) |
circle or arc | measured distance from center to circumference of a circle |
| center | center\(\mathbf{\Bigl(}\) |
circle or arc | location of the point equidistant to the edge of a circle or arc |
| coterminal | coterminal\(\mathbf{\Bigl(}\) |
angle or directed angle | angles that share an initial and terminal side (ex: 30 and -330) |
| supplement | supplement\(\mathbf{\Bigl(}\) |
directed angle | adjacent angle that forms a straight angle |
| vector.start | vector | initial/base point of a vector marker | |
| vector.end | vector | tail point of a vector marker |
Transformations
| Function | Try typing... | Arguments | This function... |
|---|---|---|---|
| dilation | dilate\(\mathbf{\Bigl(}\) |
object, then a point and a number | increases or decreases the size of an object by a specific scale factor from a given point |
| rotation | rotate\(\mathbf{\Bigl(}\) |
object, then a point and a number | turns an object about a point by a directed angle |
| reflection | reflect\(\mathbf{\Bigl(}\) |
object, then a line, segment, ray, or vector | mirrors each point in an object across a given line |
| translation | translate\(\mathbf{\Bigl(}\) |
object, then two points or a vector | moves every point of an object by the same distance in a given direction |
Learn More
- Actions
- Accessibility
- Complex Numbers
- Connections Between Geometry and Algebra
- Custom Colors
- Dynamic Labels
- Lists
- Matrices
- Sliders and Movable Points in a Graph
- Transformations: Desmos Geometry
Please write in with any questions or feedback to support@desmos.com.