This applet allows the user to explore the world of transformations, reflections, and rotations. It allows the user to translate triangles, squares, and parallelograms on both the x and y-axes.

How Do I Use This Activity?

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Controls and Output

• General Information:
  Each side 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.
• Translate Controls:
  In the appropiate spaces, type the number of units you want to translate on the X-axis and on the Y-axis. Both of these numbers must be integers. Then click the Translate button to translate the polygon.
• 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). For instance, the following example will cause a reflection across y = 3x + 2 when you click the Reflect button:
  
  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). For instance, the following example will cause a reflection across x = 3 when you click the Reflect button:
  
• Rotate Controls:
  Enter the number of degrees (an integer) you want to rotate the figure by in the appropriate box. Then, below that, enter the x and y coordinates of the point you want to rotate around. Both coordinates must be integers. Then click the Rotate button to do the rotation.
• Creating a New Polygon
  To create a new polygon, use the panel at the bottom of the screen titled "New Polygon." Enter the number of vertices you want the new polygon to have in the box labelled "How many vertices?" and click the Go! button.
  You will see a new panel containing two columns of text boxes: one for x coordinates and one for y coordinates. There are two boxes for each vertex of the polygon. Enter the coordinates of each vertex. All coordinates must be integers. If you need to see more rows, scroll down using the scroll bar on the right. When you are done, click the Finished button. The new polygon will be drawn on the coordinate plane.