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Polygons

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Use polygons to create beautiful, dynamic shapes in the Desmos Graphing Calculator, Geometry Tool, and 3D Calculator. Get started with the video to the right, then check out the example graph from the video, as well as the resources below.

Polygon Function

Graph showing \operatorname{polygon}\left((-2,2),(2,2),(0,-2)\right). Then using the polygon function and plotting points in the graph paper to create a polygon. GIF

Use the polygon function with coordinates that represent the vertices of a polygon.

Graph showing a polygon with mobable vertices. Expression line 1: A=\left(-2,2\right). Expression line 2: B=\left(2,2\right). Expression line 3:C=\left(0,-2\right) . Expression line 4:\operatorname{polygon}\left(A,B,C\right) . Screenshot.

Create a polygon with movable vertices by naming the coordinate points of each vertex of the polygon.

Image of a polygon. Expression line 1: table with coordinates (-2,2),(2,2),(0,-2). Expression line 2: \operatorname{polygon}\left(x_{1},y_{1}\right). Screenshot.

Or, create a polygon by creating a table containing the vertices of a polygon.

 

Creating a polygon with the Geometry Toolbar

Another way to create a polygon in the Desmos Geometry Tool is to use the polygon tool from the Geometry Toolbar. Once it’s selected,click on the graph paper to choose points as the vertices of the polygon. Be sure to click back to the starting point to close your polygon.

Quick tip: You can also double-click on the last vertex of your polygon to automatically close it.

Using the Geometry toolbar polygon function to plot points and create a quadrilateral and triangle. GIF.

 

Creating a Triangle in Desmos 3D

While you can’t use the polygon function in Desmos 3D, you can create a surface using three points and the triangle function.

Graph showing the triangle function to plot a triangular surface in 3D. Screenshot.

 

Transformations of Polygons

Transform polygons from the expression list or by using the transformation tools in Desmos Geometry.

In this example, the polygon is transformed using the expression list in the Graphing Calculator. It’s dilated by a factor of 2, and translated 6 units horizontally and -8 units vertically.

Click on the graph to explore polygon transformations in the Desmos Graphing Calculator.

Image of a polygon and a transformation of the polygon. Expression line 1: table with coordinates (-2,2),(2,2),(0,-2). Expression line 2: \operatorname{polygon}\left(x_{1},y_{1}\right). Expression line 3: \operatorname{polygon}\left(2\left(x_{1}+3\right),2\left(y_{1}-4\right)\right). Screenshot.

If you are working in the Geometry Tool, you can find the transformation tools in the toolbar after you select the polygon.

To learn more about transformations in the geometry tool, visit Transformations: Desmos Geometry.

Image of a polygon and a transformation of the polygon.Screenshot.

 

Polygon Option Menu

Long press the icon to the left of your expression to bring up the options menu of the polygon. From there, show/hide the outline of the polygon, change the outline opacity and width, toggle the fill on/off, and adjust the fill opacity.

Image of the polygon option menu. Screenshot.

Learn More

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