9-3: rotations rigor: students will rotate figures about a point on and off the coordinate plane....

9-3: RotationsRigor: Students will rotate figures about a

point on and off the coordinate plane.

Relevance: Rotations describe movement.

Rotations• Turn to page 383-384 in your core book and

highlight:

• A rotation turns all points about a point called the center of rotation.

• Rotation is always counterclockwise unless otherwise specified

• Function Notation: r (Q, xo) (pre-image)

center of rotation angle of rotation

• A Rotation is: a rigid transformation, image is the same distance from center as pre-image, all points rotate to image by the same angle of rotation.

Exploration• On a piece of graph paper, use a straight edge to

draw a coordinate plane with ΔABC with coordinates A(2,3), B(7, 8), and C(4, 5).

• Place a piece of scratch paper on top of Δ ABC and trace it, forming Δ A’B’C’.

• Place your pencil on C (center of rotation) and turn ΔA’B’C’. Notice how ΔA’B’C’ moves in relation to ΔABC.

• Now let the origin be the center of rotation. How does the triangle move differently?

Special Rotations in the Coordinate PlaneHighlight on pg 385, add function notation

Examples from the core book

• Rotating about the origin: EX 3 pg 385 (Label vertices A, B, C, D)

• Also rotate ABCD 90o and 1800

• Rotating about another point: EX 2 pg 384 (use tracing paper to check!)

Rotations in Regular Polygons

• A regular polygon has congruent sides and congruent interior angles.

• You can divide any regular polygon into congruent triangles.

• When you rotate a regular polygon about its center, the sides will line up when you rotate it a certain number of degrees, called the central angle.

ExamplePoint X is the center of the regular polygon PENTA. What is the image for the given rotations?

A) 72o rotation of E about X.

B) r (216o, X) ()

Real Life Example

The London Eye observation wheel takes 30min to make a complete rotation. What is the angle of rotation of a car after 5 minutes? How many minutes would it take for the car to rotate 270o?

9-3 Classwork/Homework• 9-3 Classwork from the core book:

• pg 386-387 #1 – 3, 5 – 8

• 9-3 Homework from the core book:

• Pg 389 #5 – 10

• Pg 390 #1, 3, 4, 5, 7