Quantitatively defining rigid transformations

The  exercise appears under the Geometry Math Mission. This exercise explores the quantitative properties of transformations and applications.

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


 * 1) ''Find the transformation and move a point": This problem provides a grid with a specific type of transformation pictured. The student is asked to use the grid to find the specifics of the transformation, and also find the image of a particular point under the transformation.Quandrt1.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) Calculator programs can be written that will perform some of the mechanical work.
 * 3) For reflections:
 * 4) Find the midpoint between preimages and images. These points will lie on the reflection line.
 * 5) For rotations:
 * 6) Find the intersection of the perpendicular bisectors of the images and preimages. This will be the center of the rotation. The angle can then be found by counting.
 * 7) For translations:
 * 8) Count the vertical and the horizontal shifts separately
 * 9) For dilations:
 * 10) Find intersection of lines from image to preimage. This is the center. Then the scale factor can be found by ratios.

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.