The Performing transformations on the coordinate plane exercise used to appear under the Geometry Math Mission. This exercise further analyzes rigid transformations and asks reasoning questions based on these functions.
Types of Problems
There are two types of problems in this exercise:
- Perform the rotation/translation/reflection and answer some questions: This problem asks the user to think about what happens when a certain rigid transformation is performed. They are asked to solve problems based on the transformation described.
- Create the image after the reflection/translation/rotation: This problem provides a grid, a shape, and a transformation. The user is asked to move the points on the grid to create the image that would result from the transformation.
Strategies
Knowledge of the basic rigid transformations (translation, rotation, and reflection) and ability to work well geometrically and algebraically on the coordinate plane will assist with completion of this exercise.
- Matrices could be utilized for the problem about finding coordinates but without performing the rotation.
Real-life applications
- Knowledge of the Rigid transformations can be used to understand the Erlanger Programm, a method for developing and classifying non-Euclidean geometries.
- Symmetry is a useful concept in art.
- The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.