1. What is similar about these objects?
What do we need to pay attention to when objects are rotated?

2. What am I learning today? What will I do to show that I learned it?
Course 2
8-10
Transformations
What am I learning today?
Rotations
What will I do to show that I learned it?
Determine coordinates and quadrant resulting from a rotation.

3. How do you determine the angle of rotation?
A full turn is a 360° rotation.
A quarter turn is a 90° rotation.
360°
90°
A half turn is a 180° rotation.
180°
270°
A three quarter turn is a 270° rotation.
What are they rotating around?

4. What do I need to know to complete a rotation?
Course 2
8-10
Rotations
QUESTION
What do I need to know to complete a rotation?

5. To rotate: - the direction – CW or CCW - the degrees – 90o, 180o, 270o
Course 2
8-10
Rotations
To rotate:
- the direction – CW or CCW
- the degrees – 90o, 180o, 270o
- the center or point of rotation – origin or point inside the object

6. How do I rotate an object in the coordinate plane?
Course 2
8-10
Rotations
QUESTION
How do I rotate an object in the coordinate plane?

7. To Rotate 180o around origin: 1. Keep your x- and y-values the same.
Course 2
8-10
Rotations
To Rotate 180o around origin:
1. Keep your x- and y-values the
same. .
2. Move to the opposite quadrant.
I to III III to I
II to IV IV to II
3. Put the appropriate signs
based on the quadrant.

8. Start: A (-4,3) in quadrant II Rotate 180o clockwise
Course 2
8-10
Rotations
Start: A (-4,3) in quadrant II
Rotate 180o clockwise
Finish: In quadrant IV, so x is
positive and y is
negative.
A’ (4,-3)

9. To Rotate 90o or 270o around origin: 1. x- and y-value switch places.
Course 2
8-10
Rotations
To Rotate 90o or 270o around origin:
1. x- and y-value switch places.
x becomes y and y becomes x. .
2. Find the quadrant. Move one
for 90o or three for 270o. Pay
attention to the direction.
3. Put the appropriate signs
based on the quadrant.

10. Start: A (-4,3) in quadrant II Rotate 270o clockwise
Course 2
8-10
Rotations
Start: A (-4,3) in quadrant II
Rotate 270o clockwise
Finish: In quadrant III, so x is
negative and y is
negative.
A’ (-3,-4)

11. Rotations 8-10 Rotations Around the Origin
Course 2
8-10
Rotations
Rotations Around the Origin
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 90° counterclockwise about the origin.
The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). x y A B C 3 –3 C’ B’ A’
The coordinates of the image of triangle ABC are A’(0,1), B’(-3,3), C’(0, 5).
Remember: A 90 degree rotation x and y change places, then pay attention to the characteristics of the quadrants.

12. Rotations 8-10 Rotations Around the Origin
Course 2
8-10
Rotations
Rotations Around the Origin
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 180° counterclockwise about the origin.
The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). x y A B C 3 –3
The coordinates of the image of triangle ABC are A’(-1, 0), B’(-3,-3), C’(-5, 0). C’ B’ A’
Remember: A 180 degree rotation only changes the signs, so pay attention to the characteristics of the quadrants.

13. Rotations 8-10 Rotations Around the Origin
Course 2
8-10
Rotations
Rotations Around the Origin
Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0).
Rotate ∆ABC 270° counterclockwise about the origin.
The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0). x y A B C 3 –3
The coordinates of the image of triangle ABC are A’(0,-1), B’(3,-3), C’(0,-5). C’ B’ A’
Remember: A 270 degree rotation x and y change places, then pay attention to the characteristics of the quadrants.

14. K I M
rotation

15. Practice Rotate P 270o CCW P’(3, -6) Rotate C 90o CW Rotate D 180o CW
Using these three points: P(6,3); C(-2,- 4); D(-1,0)
Rotate P 270o CCW
Rotate C 90o CW
Rotate D 180o CW
Rotate P 270o CW
Rotate C 180o CCW
Rotate D 90o CW
P’(3, -6)
C’(-4,2)
D’(1,0)
P’(-3,6)
C’(2,4)
D’(1,0)

16. Practice
Graph the pre-image, then rotate 90, 180, and 270 degrees counterclockwise P Q R

17. Now Try These
Graph Triangle MNL with vertices M(0,4), N(3,3), and L(0,0). Rotate 90 degrees clockwise.
Graph Triangle ABC with vertices A(-3, -1), B(-3, -2), and C(1, -2). Rotate 90 degrees clockwise.