Section 4.3 Rotations Student Learning Goal: Students will identify what a rotation is and then graph a rotation of 90, 180 or 270 degrees on a coordinate.

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Section 4.3 Rotations Student Learning Goal: Students will identify what a rotation is and then graph a rotation of 90, 180 or 270 degrees on a coordinate plane. Students will also be able to do composition rotations and identify rotational symmetry. Homework: Worksheet

Rotations: A rotation is a transformation in which a figure is turned about a fixed point called the center of rotation. Rays drawn from the center of rotation to a point and its image form the angle of rotation. In this chapter we are dealing with 90, 180 and 270 degree rotations. Rotations can be clockwise or counterclockwise. In this chapter, all rotations are counterclockwise unless otherwise noted. Quadrants in a Coordinate Plane: II I ( -, +) ( +, +) ( +, -) ( -, -) IV III

Coordinate Rules for Rotation about the Origin Original (Pre-Image) New (Image) Sample (Original to New) 90 degrees ( a , b) ( -b , a) (4, 6) to (-6, 4) 180 degrees (a , b) ( -a , -b) (4,6) to (-4, -6) 270 degrees (b , -a) (4,6) to (6, -4)

Example 2: Graph RSTU with vertices R(3,1), S(5,1), T(5, -3), U(2,-1) and its image after a 270 degree rotation about the origin. R S U T

Example 3: Write a rule to describe each transformation A) B)

Example 3: Graph RS with endpoints R(1, -3) and S(2, -6) and its image after the composition: Reflection: in the y-axis Rotation: 90 degrees about the origin R S

Example 4: Does the figure have rotational symmetry Example 4: Does the figure have rotational symmetry? If so, describe the rotation that maps the figure onto itself.

Example 5: