How
to make a reflector alien. themathlab.com 2001 
Step 1: print
out a copy of our large grid HERE. 

Step 2: Draw the x and a y axes in the center of the grid, and label them. 
Step 3: Now fold your paper along the x and the y axes so that only quadrant I is showing. 

Step 4: Draw the top right quarter of your alien figure. Do not lift your pencil as you draw this continuous border. Don't worry about making it look like anything in particular. Just let your pencil flow freely. Be sure your figure starts
and stops on an axis point. 
Step 5: Now mark 15 points on your border. Try to place them at key points where the shape changes direction. Label each of your 15 points with its coordinates. 

Step 6: Now reflect each of these 15 points over the y axis and label the image or prime points. As you find these reflection guide points, connect them with the reflected curves in the same way as in quadrant I. 

Step7: Now reflect a second time. Take your image points from step 6 and reflect them over the x axis. This will give you the double prime points of a double reflection. Be sure to label them with their coordinates, and draw in the connecting curves as you go. 

Step 8: Reflect the image points from step 7 and reflect them over the y axis into the fourth quadrant. These will be known as the triple prime points because they result from reflecting the original point 3 times. Be sure to label them with their coordinates, and draw in the connecting curves as you go. *You can check your math by reflecting these triple prime points over the x axis. They should fall, or "map" right on top of the original 15 points. 

Step 9: Now it's time to draw in the details like eyes, hair, hands, fingernails, ears, mouths, etc. Have fun, be creative. Add lots of bright colors for an impressive alien, and don't forget to reflect each body detail into all quadrants. 
Step 10: To add a classy bonus to your alien, print your name in quadrant I and then reflect it into each of the other three quadrants.  
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