10/27/16- Rotations and Transformations Practice (Sub Videos)

[Give students 5 minutes to copy and complete warm-up, then scroll down to show them the answers below]

Warm-Up

Create a function “(x,y) ->” to describe each transformation, then name/describe each transformation (in words). (For example: (x, y)-> (-y, -x), Reflection across y= -x)

1.) F(-2,-2) to F'(2, -2)

2.) K(0,0) L(0, 4) M(3, 4) to L'(4, 0) M'(4, 3) K'(0, 0)

3.) Z (0, 1) to Z'(-2, -3)

 

 

 

Answers:

  1. (x, y) -> (x+4, y) [Translation 4 units right] OR (x, y) -> (-x, y) [Reflection across the y-axis]
  2. (x, y) -> (y, x) [Reflection across y=x]
  3. (x, y) -> (x-2, y-4) [Translation 2 units left, 4 units down]

[Students now take these notes below]

Rotations– Rigid motion, described by 1.) Degrees of rotation 2.) Direction of Rotation (Clockwise [CW] or Counterclockwise [CCW]) and 3.) Point of Rotation

Key Ideas: 1.) The distances from the point of rotation to a preimage point and its image are equal. 2.) The angle formed from a preimage point, to the point of rotation, to its image, is the angle of rotation. [These ideas/statements will make more sense after an example from the video below]

[Watch video for example of Rotating a Triangle using Key Ideas from above (2 min)]

Rotations on the Coordinate Plane

[Students should be ready write down what is written in the video, and have their mini-graphs that were passed out on Tuesday for understanding transformations. Pass out extras to students who need them. Watch video below for explanation about how to think through developing each rule for rotations.  After video, students will copy down and complete the three rules set up below the video. Scroll down to check answers after students have had about 5 minutes to work on coming up with their own answers.]

90º Counterclockwise Rotation about the Origin

(3, 4)->

(-2, -3)->

(x, y)->

90º Clockwise Rotation about the Origin

(3, 4)->

(-2, -3)->

(x, y)->

180º Counterclockwise Rotation about the Origin

(3, 4)->

(-2, -3)->

(x, y)->

[Answers]

90º Counterclockwise Rotation about the Origin

(3, 4)->(-4, 3)

(-2, -3)->(3, -2)

(x, y)->(-y, x)

90º Clockwise Rotation about the Origin

(3, 4)-> (4, -3)

(-2, -3)-> (-3, 2)

(x, y)-> (y, -x)

180º Counterclockwise Rotation about the Origin

(3, 4)-> (-3, -4)

(-2, -3)-> (2, 3)

(x, y)-> (-x, -y)

[Pass out yellow worksheet, watch videos for examples of problems 1 (4 min), 7 (2 min), 9, and 11 (5 min)]

[Students work on the Yellow sheet until there is 15 minutes left, then pass out green sheet and watch the corresponding videos below.]

[Last 15 minutes: pass out Green worksheet, watch videos for examples of problems 3 (2 min) and 4 (3 min)]

Worksheets will be due on Monday.

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