How Do I Use This Activity?

This applet allows the user to explore the world of transformations, reflections, and rotations. It allows the user to transform polygons with up to 12 user defined vertices on the coordinate plane.

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Controls and Output

• General Information:
  Each vertex of the polygon is colored a different color to help you see the orientation of the polygon. Whenever you perform a translation, reflection, or rotation the polygon is redrawn in its new position and orientation, and a "ghost" polygon is drawn in gray in the previous position. This will help you remember where the polygon was before the transformation.
• Creating a New Polygon
  To create a new polygon, use the panel next to the coordinate plane titled "New Polygon." Enter the number of vertices (between 3 and 12) you want the new polygon to have in the box labeled "How many vertices?" and click the Go! button.
  
  You will then see a new panel containing two columns of text boxes: one for x coordinates and one for y coordinates.
  
  Enter the coordinates of each vertex. All coordinates must be integers. When you are done, preview the shape in the coordinate plane by clicking on the button. If you want to change the number of vertices, click on the button. This new polygon will be drawn on the coordinate plane:
  
  If you are not satisfied with this shape and wish to return to the orginal shape, press .
• Translate Controls:
  In the appropriate spaces, type the number of units you want to translate the shape on the X-axis and on the Y-axis. The panel is under the coordinate plane and it looks like:
  
  Both of these numbers must be integers. Then click the button to translate the polygon. The translation will appear on the coordinate plane like:
  
• Reflect Controls:
  To reflect across a non-vertical line, click the circle beside the words "across y = " and then enter the slope and y-intercept of the line you want to reflect across (both of these numbers must be integers). This is located below the coordinate plane. For instance, the following example will cause a reflection across y = 2x + 5 when you click the button:
  
  The graph of this reflection is:
  
  To reflect across a vertical line, click the circle beside the words "across x = " and enter the x-coordinate of the line you want to reflect across (this number must be an integer). Again, this is located under the coordinate plane. For instance, the following example will cause a reflection across x = 3 when you click the button:
  
  The graph of this reflection is:
  
• Rotate Controls:
  Enter the number of degrees (an integer) for a rotation of the polygon in the appropriate box. Then, below that, enter the coordinates of the center of rotation. The x and y values must be integers. Then click the button to do the rotation. The panel looks like:
  
  The graph of this rotation is: