Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Teacher Lesson Plan
Lesson:
Day 6 – Supplement Lesson
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
CC Standards
8.G.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional
figures using coordinates.
Objective
TSW… Graph and Describe 90° and 270° rotations about the origin.
Mathematical Practices
#1 Make sense of problems and persevere in solving them.
#6 Attend to precision.
#7 Look for and make use of structure.
#8 Look for and express regularity in repeated reasoning.
Note to teachers:
Be sure to teach this lesson from the PowerPoint, not the student notes. You will be missing part of the
lesson otherwise.
Teacher Input
Bellwork:
Review bellwork.
Homework: Review important problems assigned the previous night.
Introduction: Introduce as directed on the PowerPoint.
Lesson:
Teach as directed in the PowerPoint. Be sure to look at the notes on each slide for additional
instruction and answers.
Practice
Classwork
Homework
Click on each link below to watch a YouTube video that explains how to graph using rules (around origin).
180 degree rotations (3:58)
90 degree clockwise rotations (13:33)
90 degree CCW rotations (12:57)
https://www.youtube.com/watch?v=8ZeeDYIlNFk
https://www.youtube.com/watch?v=LwGmA9F3hbw
https://www.youtube.com/watch?v=4Q70ZHVFKPc
Note… The above videos are included in the PowerPoint so that you can show them to your students if you are able to.
The last two videos are longer. There is a portion at the end of the video that you can skip if necessary.
All 3 rotations:
https://www.youtube.com/watch?v=9dSnm6CSoSs
Note…This video can be shown on a Review Day.
1|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Section 1:
Rotating 90º about the Origin
Student Notes
Guided Practice #1
You Try #2
Rotate ∆EFG 90º clockwise.
Rotate ∆QRS 90º clockwise.
Pre-image
Image
Guided Practice #2
Rotate Figure EFGH 90° counter-clockwise.
Pre-image
Image
Pre-image
Image
You Try #2
Rotate Figure EFGH 90° counter-clockwise.
Pre-image
Image
2|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Using RULES to Rotate 90° about the Origin.
90 º CLOCKWISE
RULE:
 Swap the x and y values;
 Change the sign of the 2nd coordinate
to the opposite.
(x, y) → (y, -x)
EXAMPLE:
Pre-image
Image
A(3, 5)
A’(5, -3)
B(4, 1)
B’(1, -4)
C(2, 1)
C’(1, -2)
90º COUNTER-Clockwise
RULE:
 Swap the x and y values;
 Change the sign of the 1st coordinate
to the opposite.
(x, y) → (-y, x)
EXAMPLE:
Pre-image
Image
A(1, 2)
A’(-2, 1)
B(2, 3)
B’(-3, 2)
C(3, 1)
C’(-1, 3)
Rules for Rotating 270º

If asked to rotate 270° clockwise… use the rule for 90° CCW.

If asked to rotate 270° counter-clockwise… use the rule for 90° clockwise.
3|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Guided Practice #3
You Try #3
Rotate ∆EFG 90º clockwise.
Rotate ∆QRS 90º clockwise.
Pre-image
Image
Guided Practice #4
Rotate Figure EFGH 90° counter-clockwise.
Pre-image
Image
Pre-image
Image
You Try #4
Rotate Figure EFGH 90° counter-clockwise.
Pre-image
Image
4|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Classwork
Name______________________________________
Date________ Period ____
90° Rotations
1)
2)
3)
4)
5|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
5)
6)
6|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Homework
7|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
8|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Section 1: Rotating 90º about the Origin
Student Notes
Guided Practice #1
Rotate ∆EFG 90º clockwise.
You Try #2
Rotate ∆QRS 90º clockwise.
Guided Practice #2
Rotate Figure EFGH 90° counter-clockwise.
You Try #2
Rotate Figure EFGH 90° counter-clockwise.
Pre-Image
E(-4, 5)
F(-3, 2)
G(-1, 2)
H(2, 4)
Image
E’(-5, -4)
F’(-2, -3)
G’(-2, -1)
H’(-4, 2)
Pre-Image
E(-6, -6)
F(-1, -6)
G(3, -3)
H(-3, -3)
Image
E’(6, -6)
F’(6, -1)
G’(3, 3)
H’(3, -3)
9|Page
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Using RULES to Rotate 90° about the Origin.
90 º CLOCKWISE
RULE:
 Swap the x and y values;
 Change the sign of the 2nd coordinate
to the opposite.
(x, y) → (y, -x)
EXAMPLE:
Pre-image
Image
A(3, 5)
A’(5, -3)
B(4, 1)
B’(1, -4)
C(2, 1)
C’(1, -2)
90º COUNTER-Clockwise
RULE:
 Swap the x and y values;
 Change the sign of the 1st coordinate
to the opposite.
(x, y) → (-y, x)
EXAMPLE:
Pre-image
Image
A(1, 2)
A’(-2, 1)
B(2, 3)
B’(-3, 2)
C(3, 1)
C’(-1, 3)
Rules for Rotating 270º

If asked to rotate 270° clockwise… use the rule for 90° CCW.

If asked to rotate 270° counter-clockwise… use the rule for 90° clockwise.
10 | P a g e
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Guided Practice #3
Rotate ∆EFG 90º clockwise.
You Try #3
Rotate ∆QRS 90º clockwise.
Guided Practice #4
Rotate Figure EFGH 90° counter-clockwise.
You Try #4
Rotate Figure EFGH 90° counter-clockwise.
Pre-Image
E(-4, 5)
F(-3, 2)
G(-1, 2)
H(2, 4)
Image
E’(-5, -4)
F’(-2, -3)
G’(-2, -1)
H’(-4, 2)
Pre-Image
E(-6, -6)
F(-1, -6)
G(3, -3)
H(-3, -3)
Image
E’(6, -6)
F’(6, -1)
G’(3, 3)
H’(3, -3)
11 | P a g e
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)

Homework
12 | P a g e
Graphing and Describing 90° and 270° Rotations about the Origin (0, 0)
Classwork answer key not provided.
13 | P a g e