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

2022
Views:

115

Pages:

4
Author:

alliecat373za

4.3 Rotations In your own words, write the meaning of each vocabulary term. rotation: a transformation around a fixed center center of rotation: point of rotation for an object angle of rotation: the angle the object is moved rotational symmetry: when an object can be spun and still get the same image (less than 180°) center of symmetry: point where an object is spun around Core Concepts Coordinate Rules for Rotations about the Origin When a point (a, b) is rotated counterclockwise about the origin, the following are true: For a rotation of 90°: (a, b) → (-b, a) For a rotation of 180°: (a, b) → (-a, -b) For a rotation of 270°: (a, b) → (b, -a) Postulate 4.3 Rotation Postulate A rotation is a rigid motion. The image has to be exactly the same: shape size angle ⇒ congruent 4.3 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° Trick is to follow the rotation rule one point at a time J'(-2, 4) K'(5, 1) L'(2, 2) M'(1, -1) 2. 90° R'(0, -4) S'(-5, -1) T'(-1, -5) 3. 270° A'(4, -1) B'(3, -4) C'(1, -3) 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 M(4, 1) -> M'(-4, -1) -> M''(4, 1) N(-1, -2) -> N'(1, 2) -> N''(-1, -2) 5. Rotation: 90° about the origin Translation: (x, y) -> (x+2, y-5) M(-2, -1) -> M'(1, -2) -> M''(3, -5) N(3, 1) -> N'(-1, 3) -> N''(1, 0) 6. Rotation: 270° about the origin Reflection: in the line y = x M(3, 4) -> M'(4, -3) -> M''(-3, 4) N(1, 3) -> N'(-3, 1) -> N''(1, -3) 7. Rotation: 90° about the origin Translation: (x, y) -> (x-5, y) M(3, 3) -> M'(3, -3) -> M''(-2, -3) N(1, 0) -> N'(0, 1) -> N''(-5, 1)