This document provides an overview of transformational geometry concepts for a test prep lesson, including definitions, examples, and practice problems. It reviews translations, reflections, rotations, and dilations by defining key terms, presenting rules and notation, and working through example problems. Students are instructed to complete a transformations packet in pairs during class and a test on these concepts will be given shortly. Reviewing notes and practice problems is recommended to prepare.

1. Test Prep #10: Transformational
Geometry
EQ: How can we review and improve our test
prep skills of transformational geometry
including: translations, reflections, rotations, and
dilations?
Do Now: (3 minutes)
Define “Transformational GeometryTransformational Geometry”.

2. Vocabulary
Transformation – Some sort of change/edit.
Pre-Image – Original/non-transformed figure.
Image – The new & transformed figure.
Origin – Point (0, 0)(0, 0) on a coordinate plane.
Geometry – Mathematical area/subject of
shapes and figures.

3. Translations
-Moving the figure on the coordinate plane
either up, down, left, and/or right.
-Arrow Notation Rule is (x, y) → (x + ?, y + ?)
Example: Translate this figure 3 units leftleft and 2
units upup, also find the rule! (3 minutes)

4. Translations Example: Answer
3 units left and 2 units up would lead to the
points of the new image being at (0, 0), (-2,
0), (-2, -2), and (0, -3). The arrow notation
rule here would be (x, y) → (x – 3, y + 2)(x, y) → (x – 3, y + 2).

5. State Exam
Test Prep
Question!

6. Reflections
-Reflecting the figure over some point or line,
usually “over the x-axis” or “over the y-axis”.
-If it's “REFLECT OVER THE X-AXIS”, then
you keep the x value but the y value turns
to it's opposite symbol. (ex: negative to
positive, and positive to negative).
-If it's “REFLECT OVER THE Y-AXIS”, then
you keep the y value but the x value turns
to it's opposite symbol. (ex: negative to
positive, and positive to negative).

7. Reflections: Using Arrow Notation
Over the xx-axis: (x, y) → (x, –y)
Over the yy-axis: (x, y) → (–x, y)

8. Reflections Examples
#1) Reflect across #2) Reflect across
the y-axis y = x

9. Reflections Examples: Answers
#1) Reflect across #2) Reflect across
the y-axis y = x

10. Rotations
-Rotating the figure on the coordinate plane.
-We can rotate CLOCKWISECLOCKWISE or
COUNTERCLOCKWISECOUNTERCLOCKWISE.
-Usually turning 0°, 90°, 180°, 270°, or 360°.
-The two “D's” of rotations are DEGREE (how
far) and DIRECTION (which way).
-Image is still CONGRUENT when rotated.
-Usually it would ask to “Rotate about the
origin”.

11. Rotations “about the origin”:
Using Arrow Notation
Counterclockwise Clockwise
90°
(x, y) → (–y, x)(x, y) → (–y, x) (x, y) → (y, –x)(x, y) → (y, –x)
180°
(x, y) → (–x, –y)(x, y) → (–x, –y) (x, y) → (–x, –y)(x, y) → (–x, –y)
270°
(x, y) → (y, –x)(x, y) → (y, –x) (x, y) → (–y, x)(x, y) → (–y, x)
360°
(x, y) → (x, y)(x, y) → (x, y) (x, y) → (x, y)(x, y) → (x, y)

12. Rotations: Example
Rotate 90 degrees clockwise about the origin:
U(1, –2), W(0, 2), K(3, 2), G(3, –3)

13. Rotations: Example Answer
Rotate 90 degrees90 degrees clockwiseclockwise about the origin:
U(1, –2), W(0, 2), K(3, 2), G(3, –3)
U(1, –2) → U'(–2, –1)
W(0, 2) → W'(2, 0)
K(3, 2) → K'(2, –3)
G(3, –3) → G'(–3, –3)

14. Visual: Rotations Summary

15. Dilations
-A transformation that produces an image that
is the SAME SHAPE as the original but NOTNOT
THE SAME SIZE! (Basically like resizing)
-A dilation is SIMILARSIMILAR to the original figure.
-Dilations are centered around the origincentered around the origin,
unless otherwise stated.
-Scale Factor is a ratioratio from (image length)/
(pre-image length)
-ARROW NOTATIONARROW NOTATION is (x, y) → (fx, fy)
f representing the scale factorscale factor ^

16. Dilations: Scale Factor
The figure either gets LARGER, SMALLER,
or STAYS THE SAME.
If the scale factor is greater than 1, then
your figure gets largerlarger.
If the scale factor is less than 1, then your
figure gets smallersmaller.
If the scale factor is equal to 1, then your
figure's size stays exactly the samestays exactly the same with no
changes.

17. Dilations: Examples
1) If the scale factor 2) Dilate this figure with
is 33, how would the scale factor of ½½.
you write this
rule in arrow
notation?

18. Dilations: Examples Answers
1) If the scale factor 2) Dilate this figure with
is 33, how would the scale factor of ½½.
you write this
rule in arrow
notation?
(x, y) → (3x, 3y)

19. Classwork: Work in Pairs!
Work: CompleteComplete the Transformations Packet.
Look back at your notes or use your
partner's assistance if needed. It is
recommended that you two split the
work up to get this done faster. Show
your work! Good Luck! :)
Time: 22 Minutes (20 minimum, 25 maximum)
Any Questions/Concerns? Ask the teacher.Any Questions/Concerns? Ask the teacher.

20. Classwork Review
Let's go over the answersanswers
together as a class! Pay
attention! If you were not
able to completely finish,
work through as we go over
it please. =)

21. Math Song: “Transformation Style”
Song Name: “Transformation Style”
Song Creator: RHYTHMetric
Parody of: “Gangnam Style” by PSY
Source: YouTube
Link: https://www.youtube.com/watch?https://www.youtube.com/watch?
v=NKtJd1hkI9kv=NKtJd1hkI9k
Enjoy!!! =D

22. Incoming Test: Transformational
Geometry!
THERE WILL BE A FINAL TESTTEST ON
“Transformational GeometryTransformational Geometry” THE DAY
AFTER THE NEXT DAY WE MEET. IT IS
HIGHLY RECOMMENDED THAT YOU
STUDY AND REVIEW YOUR NOTES OF
THIS LESSON AS WELL AS THE
CLASSWORK ASSIGNMENT YOU WERE
SUPPOSED TO COMPLETE. IT WILL NOT
BE A BIG TEST, BUT IT WILL STILL BE
GRADED! GOOD LUCK! =D

23. Homework
Written Homework: No written homework.
Extra Homework: FinishFinish anything that was not
finished as classwork!!!
Upcoming Things: Study/Review for the final
test on “Transformational Geometry” about
this lesson. The test is the day after the next
day we meet. Good Luck! Also, the next
lesson is a topic in 3-D Figures3-D Figures.