2/14/2017
Prebell
1. Describe the
transformation.
Rotations
2. Find the coordinates of the
image of the figure
𝑄 −1, −5 , 𝑅 −1, −1 , 𝑆 4, 0 ,
and 𝑇(4, −5) after a
reflection about the origin.
• Rotation – change in orientation; turn about a
point called the center of rotation
• The number of degrees rotated is the angle of
rotation.
Rules for Rotations
Partner Activity Introducing Rotations
• The direction of rotation is important.
Counterclockwise Rotations
• 90°: (𝑥, 𝑦) → (−𝑦, 𝑥)
• 180°: 𝑥, 𝑦 → −𝑥, −𝑦
• 270°: (𝑥, 𝑦) → (𝑦, −𝑥)
Clockwise Rotations
• 90°: (𝑥, 𝑦) → (𝑦, −𝑥)
• 180°: 𝑥, 𝑦 → −𝑥, −𝑦
• 270°: (𝑥, 𝑦) → (−𝑦, 𝑥)
What do you notice?
•
•
Practice Rotating About the Origin
𝑀(−3, −2) rotated 90° CW
𝑄(−4, 6) rotated 180°
𝑁(0, −4) rotated 180°
𝑅(7, −1) rotated 270° CW
𝑃(1, 3) rotated 270° CCW
𝑆(5, 0) rotated 90° CCW
180° rotations are the same in any direction.
90° rotations and 270° rotations (in the opposite
direction) give the same image.
Shortcut
Plot the following points on your graph paper:
𝐴 1, 5
𝐵 2, 1
𝐶 (−3, −1)
1
2/14/2017
Shortcut
• Rotate your paper in ¼ turns.
– Counterclockwise turns left ←
– Clockwise turns right →
90° – turn 1 time
180° – turn 2 times
270° – turn 3 times
360° – turn 4 times
(ends up back
where you started)
Practice Rotating About the Origin
Rotate 90° CCW
Rotate 180°
• Identify each ordered pair using the new
(rotated) axes.
• Turn your paper back to its original position.
• Graph the image using the points you
identified by turning your paper.
HW: Rotations on a Coordinate Plane
• Use Rotation Rules for Ordered Pairs (top half)
• Use Shortcut for Graphs (bottom half)
2