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”.

VocabularyTransformation – 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.

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)

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).

State Exam Test Prep Question!

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).

Reflections: Using Arrow Notation

Over the xx-axis: (x, y) → (x, –y)

Over the yy-axis: (x, y) → (–x, y)

Reflections Examples#1) Reflect across #2) Reflect across

the y-axis y = x

Reflections Examples: Answers#1) Reflect across #2) Reflect across

the y-axis y = x

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”.

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)

Rotations: ExampleRotate 90 degrees clockwise about the origin:

U(1, –2), W(0, 2), K(3, 2), G(3, –3)

Rotations: Example AnswerRotate 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)

Visual: Rotations Summary

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 ^

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.

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?

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)

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.

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. =)

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=NKtJd1hkI9k v=NKtJd1hkI9k

Enjoy!!! =D

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

HomeworkWritten 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.