on and off the coordinate plane Relevance Rotations describe movement Rotations Turn to page 383384 in your core book and highlight A rotation turns all points about a point called the ID: 701909
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Slide1
9-3: Rotations
Rigor
: Students will rotate figures about a point
on and off the coordinate plane.
Relevance:
Rotations describe movement.Slide2
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 specifiedFunction Notation: r (Q, xo) (pre-image) center of rotation angle of rotationA 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.Slide3
Exploration
On a piece of graph paper, use a straight edge to draw a coordinate plane with
Δ
ABC 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? Slide4
Special Rotations
in the Coordinate Plane
Highlight on
pg 385, add function notationSlide5
Examples from the core book
Rotating about the origin: EX 3
pg
385 (Label vertices A, B, C, D)Also rotate ABCD 90o and 1800Rotating about another point: EX 2 pg 384 (use tracing paper to check!)Slide6
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.Slide7
Example
Point 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) () Slide8
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 270
o
?Slide9
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 – 10Pg 390 #1, 3, 4, 5, 7