Perform rotations

The  exercise appears under the 8th Grade Math Mission. This exercise presents the geometric transformation of rotation.

Types of Problems
There are two types of problems in this exercise:


 * 1) Rotate the shape as specified: This problem provides a grid with an orange polygon and a rotation. The student is asked to use the manipulative to rotate the polygon as requested.Rop1.png
 * 2) Define the rotation pictured: This problem provides a grid with an orange pre-image and a blue image. The student is asked to define the rotation that moves the orange polygon onto the blue.Rop2.png

Strategies
An ability to read the coordinate plane and knowledge of the notation for rotations are all that is needed to perform this problem accurately and efficiently.
 * 1) A rotation T_x represents a rotation of an angle of x, counterclockwise, about the origin.
 * 2) The angles of rotation are one of 90 degrees, 180 degrees and 270 degrees.
 * 3) The 90 degree rotation can be confused with the 270 degree rotation because a 270 degree rotation is a 90 degree rotation but in a clockwise (backward) direction.
 * 4) Angles are always measured counterclockwise in mathematics because the initial starting measure is the positive x-axis, making it reasonable to move upward into quadrant one.

Real-life applications

 * 1) Rotation matrices in linear algebra can be used to represent objects that spin.
 * 2) A rotation is an isometry (in particular a conformal map) which is useful for defining non-Euclidean geometries such as the possible hyperbolic geometry of space.