Rotations Chapter 3 Section 8 Course 3

Transformations

example: earth rotates on its axis

Motion Notation Example Translation Slide T<a, b> T<-1, 2>

Reflection Flip Rline Ry-axis

Rotation Turn rx° r90°

Rotation about a point

A rotation – is a turn oThe number of degrees an

image is rotated is called the angle of rotation.

written as rx°(P) = P’

π π

Rotation in the Coordinate Plane When a figure is rotated

90°, 180° or 270° you can use the following rules.

r90°(x,y) =(-y, x)

r180°(x,y) =(-x, -y)

r270°(x,y) =(y, -x)

Example P(-2, 3)

1. r90°(P) =

2. r180°(P) =

3. r270°(P) =

Example A(1, -2)

1. r90°(A) =

2. r180°(A) =

3. r270°(A) =

Example B(4, 1)

1. r90°(A) =

2. r180°(A) =

3. r270°(A) =

Example ABC has vertices A(1, 1), B(1, 6)

and C(4, 1).

r180°(ABC)

Example LMN has vertices L(0, 0), M(3, -5)

and N(-2, -2).

r90°(LMN)

Example L(-2, 5)

1. r90°(L) =

2. r180°(L) =

3. r270°(L) =

Example M(-1, -3)

1. r90°(M) =

2. r180°(M) =

3. r270°(M) =

Example ABC has vertices A(-2, 1), B(-2, -2)

and C(0, 0).

r270°(ABC)

Rotational Symmetry A figure has rotational symmetry if you can rotated (turn) 180° or less and it exactly matches up with the original figure.

Example:

Does the figure have rotational symmetry, reflectional symmetry or

both. 1. 2.

3. 4.