Transforming polygons

The  exercise appears under the Geometry Math Mission. This exercise has an opportunity to actually create images under transformations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Perform the specified transformation: This problem has a grid with a polygon drawn and a transformation described. The student is asked to find the image of the polygon under the transformation.Tranpoly1.png

Strategies
Knowledge of transformations and confidence with geometric reasoning and imaging are encouraged to ensure success on this exercise.
 * 1) With linear algebra and matrices, some of the problems in this exercise can be done more efficiently.
 * 2) For reflections:
 * 3) Count the horizontal and vertical spots to the reflection line at convenient points.
 * 4) Repeat the counts in reversed order in opposite direction to find images.
 * 5) For rotations:
 * 6) Count the horizontal and vertical spots to the center of rotation.
 * 7) Move that "right angle" as specified by the rotation to get the image.
 * 8) For translations:
 * 9) Count the vertical and the horizontal shifts separately from each point.
 * 10) For dilations:
 * 11) Count the distance to the center.
 * 12) Multiply by the scale factor.
 * 13) Move that new number of spots from the center.

Real-life Applications

 * 1) Art applications have need for knowledge of transformations. Many great artists were also geometric masters (Da Vinci).
 * 2) Architecture relies heavily on symmetry and transformations to create buildings.