Today’s Lesson:

What: transformations (rotations). . .

Why: To perform rotations of figures on the coordinate plane. .

Translation Review:Remember, a translation is a ______________ .

MEMORIZE: “RIGHT or LEFT changes _____!! UP or DOWN changes _____!!!

This means that if a figure moves RIGHT or LEFT, we ADD or __________________ from the original x coordinate.

If a figure moves UP or DOWN, we ADD or SUBTRACT from the original ______coordinate.

Point A, (3, 5) is translated two to the left and four up. Where is AI ?

slide

x y

SUBTRACT

y

Answer: (1, 9)

A AI

Stations of Rotation:

90º:

180º:

270º:

360º:

CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________.

COUNTER-CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________.

What about rotations ??

right

left

Let’s explore some rotations . . . Rotation Applet

turn

turn

turn

full turn

Exploring Rotations

(To be used in conjunction with NLVM)A ROTATION refers to when a geometric figure is ________________________ around

a center of rotation. For this activity, we will explore rotations on the coordinate plane. Our

center of rotation will be the ____________________________ .

Directions: As Ms. Dyson rotates the following figure (on the screen), let’s track the movement of

one point:

Rotation #1: Clockwise Rotation of Trapezoid:

Original coordinate of given point: ( , ) Quadrant: _____

Coordinate after 90°clockwise rotation: ( , ) Quadrant: _____

Coordinate after 180°clockwise rotation: ( , ) Quadrant: _____

Coordinate after 270°clockwise rotation: ( , ) Quadrant: _____

Coordinate after 360°clockwise rotation: ( , ) Quadrant: _____

Rotation #2: Clockwise Rotation of Trapezoid:

Original coordinate of given point: ( , ) Quadrant: _____

Coordinate after 90°clockwise rotation: ( , ) Quadrant: _____

Coordinate after 180°clockwise rotation: ( , ) Quadrant: _____

Coordinate after 270°clockwise rotation: ( , ) Quadrant: _____

Coordinate after 360°clockwise rotation: ( , ) Quadrant: _____

Do you notice any patterns among the coordinates above?

Rotation #3: Counter-Clockwise Rotation of Trapezoid:

Original coordinate of given point: ( , ) Quadrant: _____

Coordinate after 90°counter-clockwise rotation: ( , ) Quadrant: _____Coordinate after 180°counter-clockwise rotation: ( , )

Quadrant: _____Coordinate after 270°counter-clockwise rotation: ( , )

Quadrant: _____Coordinate after 360°counter-clockwise rotation: ( , )

Quadrant: _____

Did the patterns/ observations you made about the clockwise rotations change when we

performed the counter-clockwise rotation?

Name:________________________________________________________________Date:_____/_____/__________

Rotation Applet

Using the observations and/or patterns we just discussed, what would be a rule that we could use to

know what each new point will be without seeing the rotation on the screen?

Rule:

Now, use the above rule to record the new coordinates for the below rotation (without seeing it on

the screen).

Rotation #4: Counter-Clockwise Rotation of Trapezoid:

Original coordinate of given point: ( , ) Quadrant: _____

Coordinate after 90°counter-clockwise rotation: ( , ) Quadrant: _____Coordinate after 180°counter-clockwise rotation: ( , )

Quadrant: _____Coordinate after 270°counter-clockwise rotation: ( , )

Quadrant: _____Coordinate after 360°counter-clockwise rotation: ( , )

Quadrant: _____

Original Coordinates:

A (2, 1) B (2, 7) C (6, 1)

90º Quadrant ________

A ( , )

B ( , )

C ( , )

180º Quadrant ________

A ( , )

B ( , )

C ( , )

270º Quadrant ________

A ( , )

B ( , )

C ( , )

360º Quadrant ________

A ( , )

B ( , )

C ( , )

Rotating a triangle (together in class) . . .

A

B

CAIBI

CI

AI

BI

CI

AI BI

CI

II

III

IV

I

END OF LESSON

The next slides are student copies of the notes for this lesson. These notes were handed out in class

and filled-in as the lesson progressed.

NOTE: The last slide(s) in any lesson slideshow (entitled “Practice Work”)

represent the homework assigned for that day.

Math-7 NOTES DATE: ______/_______/_______What: transformations (ROtations). . .

Why: To perform rotations of figures on the coordinate plane.NAME:

Stations of Rotation:

90º:

180º:

270º:

360º:

CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________.

COUNTER-CLOCKWISE: from “12 o’clock” (top of coordinate graph), figure will rotate to the ____________________.

Translation Review:Remember, a translation is a __________________ .

MEMORIZE: “RIGHT or LEFT changes _____!! UP or DOWN changes _____!!! This means that if a figure moves right or left, we ADD or __________________ from the original x coordinate. If a figure moves up or down, we ADD or SUBTRACT from the original ______coordinate.

Point A, (3, 5) is translated two to the left and four up. Where is AI ?

A AI

Rotation Applet

What about rotations ??

Original Coordinates: A (2, 1) B (2, 5) C (6, 1)

90º Quadrant ________

A ( , ) B ( , ) C ( , )

180º Quadrant ________

A ( , ) B ( , ) C ( , )

270º Quadrant ________

A ( , ) B ( , ) C ( , )

360º Quadrant ________

A ( , ) B ( , ) C ( , )

Directions: Plot the original points as indicated. Connect the points to make a right triangle. Then, rotate the ORIGINAL triangle counter-clockwise as indicated:

Rotating a triangle (together in class) . . .

1. Where will Point A end up after a 90° clockwise rotation? _______

2. Where will Point A end up after a 180° clockwise rotation? _______

4. Where will Point A end up after a 270° clockwise rotation? _______

3. Where will Point A end up after a 90° counter-clockwise rotation? ______

6. Where will Point A end up after a 180° counter-clockwise rotation? _______

5. Where will Point A end up after a 270° counter-clockwise rotation? _______

A

A

A

A

A

A

Math-7 Practice/ HOMEWORK“rotations”

NAME: ________________________________________________________________________________DATE:_____/_____/__________

1) 2)

3) 4)