University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

70

Pages:

4
Author:

Beriottooiix

Rotations Section 1: Vocabulary Rotation: A transformation of an object around a fixed center. Center of Rotation: The point around which an object is rotated. Angle of Rotation: The angle through which the object is moved. Rotational Symmetry: When an object can be spun and still get the same image (less than 180°). Center of Symmetry: The point where an object is "spun" around. Section 2: Core Concepts Coordinate Rules for Rotations (Counterclockwise about the Origin): 90° rotation: (a, b) → (-b, a) 180° rotation: (a, b) → (-a, -b) 270° rotation: (a, b) → (b, -a) Postulate 4.3 Rotation Postulate: A rotation is a rigid motion. This means the image has to be exactly the same: Shape Size Angle (aka congruent) 4.3 Extra Practice In Exercises 1-3, graph the image of the polygon after a rotation of the given number of degrees about the origin. 1. 180° J(-2,4) J'(-2,-4) K(-5,1) K'(5,-1) L(-2,-2) L'(2,2) M(1,1) M'(-1,-1) Trick is to follow the rotation rule one point at a time 2. 90° R(-1,0) R'(0,-1) S(-1,5) S'(5,1) T(-5,1) T'(-1,-5) 3. 270° A(1,4) A'(4,-1) B(4,3) B'(3,-4) C(3,1) C'(1,-3) D(1,2) D'(2,-1) 4.3 Extra Practice In Exercises 4-7, graph the image of MN after the composition. 4. Reflection: x-axis Rotation: 180° about the origin 5. Rotation: 90° about the origin Translation: (x, y) → (x + 2, y - 2) 6. Rotation: 270° about the origin Reflection: in the line y = x 7. Rotation: 90° about the origin Translation: (x, y) → (x - 5, y)