Justin Fernandez Fiona McClean Sebastian Quiana Eric Spiniello and Wendy Star Table of Contents Rotations Fiona McClean Looney Tunes Reflections Wendy Starr Simpsons ID: 683698
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Slide1
Cartoon Transformations
By
: Justin
Fernandez,
Fiona
McClean
,
Sebastian
Quiana
, Eric
Spiniello
, and Wendy StarSlide2
Table of ContentsRotations – Fiona McClean
Looney TunesReflections – Wendy Starr SimpsonsTranslations – Eric Spiniello Tom and JerryTessellations – Justin Fernandez Scooby DooDilations – Sebastian
Quiana
SpongebobSlide3
Rotations
By: Fiona
McCleanSlide4
Rotations
A rotation is an isometry where shapes rotate around a fixed point in a circular motion, whether clockwise or counter clockwiseSlide5
Angle of Rotation
: rays drawn from the center of rotation to a point and its image form an angle
-If center of rotation is origin:
R
90
°
(
x,y
) = (-
y,x
)
R180° (x,y) = (-x,-y)R270° (x,y) = (y,-x)R-90° (x,y) = (y,-x)Center of Rotation: the fixed point of a rotation P Point P is the center of rotationRotational Symmetry: when a figure can be mapped onto itself by a clockwise rotation of 180 degrees or lessAn equilateral triangle can be mapped onto itself by 120 degrees
Rotations VocabularySlide6
Center of Rotation:
(0,0)
Angle of Rotation:
270
°
Vertices:
A (-4,4,) A’ (4,4)
B (-2,4) B’ (4,2)
C (-2,2) C’ (2,2)
D (-4,2) D’ (2,4)
A
B
C
D
A’
B’
C’
D’Slide7
B
A C
E D
F
Center of Rotation:
Point
F
Angle of Rotation:
80 degreesSlide8
Tweety wants to go into his cage. Rotate Tweety 110 degrees about point
P
, (9,4), so that he is in his cage. Find A’, B’, C’, D’, and E’.
Help Tweety
Vertices:
A (16.5, 7)
B (14, 6.5)
C (12.5, 7)
D (13, 9)
E (14.5, 9.5)Slide9
Real Life Application
The top of Tweety’s bird cage has
rotational symmetry
. It can be mapped onto itself at 36 degrees.Slide10
Bibliography
"Looney Tunes."
SAT 400
.
N.p
.,
n.d.
Web. 23 Apr. 2013. <http://www.sat400.com/
satlooney.html>.
"EK Success Wavy Circle Large Punch."
BGPayne
Crafts. N.p., n.d. Web. 23 Apr. 2013. <http://www.bgpaynecrafts.co.uk/products/ 21307-ek-success-wavy-circle-large-punch.aspx>. Slide11
Reflections
By: Wendy StarSlide12
Vocabulary
Reflection – an image over a line, that almost acts like a mirror.
Line of Reflection – the which acts like a mirror in a reflection.
Line of symmetry – a figure that can be mapped onto itself by a reflection in the line.
Isometry – transformation which the two figures are congruent.Slide13
Line of Symmetry
3 Sides
3 Lines
4 Sides
2 Lines
4 Sides
4 Lines
3 Sides
1 Line
In a regular polygon, the number of lines of symmetry is equal to the number of side.
In a non regular polygon, one must
just
count.Slide14
All of their faces have one line of symmetry.Slide15
Pre-Image over line, find coordinates
Equations need:
R
x-axis
(
x,y
) = (x, -y)
R
y
-axis
(
x,y) = (-x,y)Ry=x (x,y) = (y,x)Ry=-x (x,y) = (-y,-x)Slide16
Equation Line of
Reflection
To find the line of reflection, you find the midpoints, from matching vertexes, and graph the line. That will be the line of reflection.
Line of ReflectionSlide17
Marge Simpson ReflectedSlide18
Minimum Distance
To find the minimum distance, you reflect one of the initial points (point A), then you connect A’ to point B. where that line crosses the x-axis will be the minimum distance point C.
A
B
C
A’
A (-1,5)
B (5,1)
A’ (-1,-5)
C (4,0)
What is the equation of the line A’B?Slide19
Real Life Application
If a character from the Simpsons were to look into a mirror they would see their face reflected back at them.Slide20
GSP Activity
Go onto GSP and make sure you have graph up.
Then plot A(-1,-2) and B (8,-4).
Next find the minimum distance and the equation of A’B.
Do the same for A (1,4), B (8,3).Slide21
Bibliography
All Slides:
http
://
t3.gstatic.com/images?q=tbn:ANd9GcTfjjBz37-c-6b2x_EImq34uX60zmXCwN7Pyf7x91AFdhW727Ju:upload.wikimedia.org/wikipedia/en/3/33/All_Simpsons_characters.jpg
Slide 1:
http://images1.wikia.nocookie.net/__
cb20100602025911/simpsons/images/6/65/Bart_Simpson.png
Slide 4:
https
://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcS4qxV1o2Dk4yIHd8rC5t_oMcpdrVdGk4491jfC8FDNlLKzULw9https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcQljPs8VRIbBCHfCibsqAxm3Qw0NaglTlxHWqMimdZD1z_xavY8
https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcTZn-JGnr9jvpfHqPTjslYUKPcxD3vg6eGFCtiULC5Fl7gnWkS7xwSlide 6:http
://www.regentsprep.org/Regents/math/geometry/GT1/xgraph.gifhttp://www.regentsprep.org/Regents/math/geometry/GT1/PtGraph.gifSlide 7:
https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcR9704cU93y6UevI-_uuXKUnv52ywQQh2ZkxPiH0Av4oOjUgbRuhttps://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcSn4iIp-Z4GW5FdkE62UNWhOnne5fIs1kEEWn2YzUw_bxuHqXGe
Slide 9:
http
://slacktory.com/wp-content/uploads/2011/10/Marge-vs-Girl-at-Mirror.jpg
https://
encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRtifkK3QsjzDWP92u1I3jtRYbWG1tRU_i6Yf_ph7b3agfiaHw6
Slide 10:
Chapter 7 Resource Book Lesson 7.2Slide22
Tom and Jerry’s Translations
By: Eric
SpinielloSlide23
Words to Know: Translation: a type of transformation where every point of a pre image is moved a certain distance is a certain direction to form an image. The image is congruent to the pre image, it is just moved.
Initial Point: The starting point of a vector. Terminal Point: The end point of a vectorVector: a quantity that has both magnitude and direction. Component Form: is made up by the horizontal and vertical components of a vector. For example, the rule (
x,y
)>(x+2,y-3) becomes <(2,-3)> in component form.
Coordinate notation: tells you the distance on the x and y axis you should move each point. For example, (
x,y
)>>>(
x+a,y+b
). “A” represents the amount of units you moved on the x axis and “B” represents the amount that you moved on the y axis. Slide24
Mammy Two Shoes Mathematical ExamplesIn this example, each point slides 7 units left and 3 down. This means that the rule is (
x,y)>>(x-7,y-3). In component/vector form it would be <-7,-3> and in coordinate notation (x,y)>>(x-7,y-3). Slide25
Mammy Two Shoes Mathematical ExamplesYou can also find this by using matrices. First, you must take the coordinates of A B C and D and record them in a matrix. The x coordinate plots go on the top, with the y on the bottom.
[A B C D] [A B C D] [A B C D][2 4 5 2] + [-7 -7 -7 -7] = [-5 -3 -2 -5][4 4 2 1] + [-3 -3 -3 -3] = [ 1 1 -1 -2]
Since the rule is (
x,y
)>>(x-7,y-3), we added -7 to the x coordinates and -3 to the y coordinates. This tells us that the new coordinates for the image are A’= (-5,1) B’= (-3,1) C’= (-2,-1) D’= (-5,-2)Slide26
Tom’s Translation ConceptsIf you are given a pre image at point (3,-2) and a rule (
x,y)>>(x+5,y-2) then you would start at point (3,-2) and count 5 units to the right and 2 units down on a coordinate plane. So the coordinates of the image would be (8,-4). If you are given the image at point (8,-4) and a rule (
x,y
)>>(x+5,y-2), then you would subtract 5 from 8 and add 2 to -4. This would make the coordinates of the pre image (3,-2). Slide27
Jerry’s GSP ActivityUnder graph, click “show grid”.
Create any shape of your choice. Label the points. Highlight your shape. Go to the “Transform” window and select “Translate”. On the new window select “Rectangular” under “Translation Vector”. Write in 7cm for the horizontal and 2cm for the vertical fixed distances. This will be the number of units your new image will translate.
Click “Translate”.
Your new image is a translation from the original pre image. It should look like the example. Slide28
Jerry’s GSP Activity QuestionWhat is the rule for the translation you just made?
How would you write that rule in component form? Slide29
Real World ApplicationsIn cartoons, translations are everywhere. For example, as Tom runs after Jerry, both characters are translating and moving across the screen. Slide30
Bibliographytomjerrynew.blogspot.com
(Title Photo)http://atminhd.com/tom-and-jerry-wallpaper-download-hd.html (Tom and Jerry Second Slide)http://www.regentsprep.org/Regents/math/geometry/GT2/Trans.htm
(Translation Diagram)
http://
en.wikipedia.org/wiki/Mammy_Two_Shoes
(Mammy Two Shoes)
protagonist.wikia.com
(Tom)
mugen.wikia.com
(Jerry)
http://www.goldenagecartoons.com/reviews/2008/tjtales4
/ (Tom and Jerry Confused)www.toptimelinecovers.com (Tom chasing Jerry)http://www.regentsprep.org/Regents/math/geometry/GT2/Trans.htm (Math Information)Geometry Textbook (Math Information)Slide31
Tessellations
By: Justin FernandezSlide32
What's a
Tesserration
Raggy
?
A tessellation is
the process of creating a two-dimensional
plane using
the repetition of a geometric shape with no overlaps and no
gaps
Example:
Around any vertex or corner point in a tessellation the measure of all angles must equal 360 degrees
In this case four 90 degree anglesSlide33
Jeepers Gang, look at that Tessellation!
There are many tessellations that appear everywhereThe most common being floor tilling
The tessellation made in this floor tilling is made of regular squares alternating from white to black
This is made of rectangular bricks on a wall on a street or of a house
This tessellation is know as a 4.4.4 tessellation because of the amount of shapes and their # of sides
4
4
4Slide34
Scooby DoodlesSlide35
Rings Ry Ridn’t Rake (things I didn’t make)
Slide36
How to Create a Scooby Snack (Tessellation)
Find a picture that you want to tessellate like this one. A square, rectangle, right triangle, or regular triangle would be the easiest.Start by placing it into a new Photoshop documentThe size should be U.S.
paper size which is
selected
when
you select File
New then in the
Present drop down menu select U.S.
PaperSlide37
3. To get the picture in the document copy the picture form any online source and then in the Edit drop down menu on the top left select paste and the picture should be right there.
4. After this press the Crtl key simultaneously with the T key and the picture should be able to be resized. Hold shift and on the corners adjust it to your proffered size. After this press
Crtl
and the D key
5. Move the picture with the tool by pressing v and move it to the top left leaving room in between the top and the left edge of the paper
6. Then ¾ down the right hand side there is a tab called layers select that
7. Right click the layer that says Layer 1 and select duplicateSlide38
8. The new image should appear right on top of the other one, just take this image and move it to be right next to the other one to the right
9. Keep doing this until you have enough to make a row across the paper but not touching the right edge
10. Then select on the layers tab the top most image, right click and select merge down until all you have is the one layer and the background
11. Then duplicate this layer comprised of all the copied pictures and duplicate that. Then place this copy underneath the other imageSlide39
12. Keep doing this until the whole page is filled. The final project should look somewhat like this.Slide40
Dilations
By: Sebastian
QuianaSlide41
Terms To Know
Dilation – Transformation that produces a shape that is different in size
Scale Factor – Ratio of corresponding sides of an image over a pre-image (K)
Reduction – If the scale factor is less than one
Enlargement – If the scale factor is greater than oneSlide42
Terms to know Cont.
Center of Dilation – A fixed point where all points are dilated
Equation:
Dk
(
x,y
)=(
kx,ky
)
K = OP’/OPSlide43
Properties preserved
Angle measures remain the same
(Parallelism) Parallel lines remain parallel
(
Colinearity
) Points stay on the same lines
(Midpoint) Midpoints remain the same in each figure
(Orientation) Lettering order remains the sameSlide44
Example of a Reduction
Scale Factor
1/2
A
B
c
Multiplying with Matrices
A B C
X = 5 7 3
Y = 6 3 3
1/2
A’ B’ C’
X = 2.5 3.5 1.5
Y = 3 1.5 1.5Slide45
Example of a Enlargement
Scale Factor
2
A
B
c
Enlargement
Multiplying with Matrices
A B C
X = 5 7 3
Y = 6 3 3
2
A’ B’ C’
X = 10 14 6
Y = 12 6 6Slide46
Real Life Application
It has been discovered that a full grown Box Jellyfish can be 300 cm long and 25 cm wide. It has also been found that a baby Box Jellyfish can measure 15 cm long.
Find the scale Factor of the length
Using the Scale factor find the width of the baby jellyfish
Is this a reduction or an enlargement
300 cm
15 cmSlide47
GSP Activity
First Click ‘graph’ and then click on ‘form grid’
Next Create a triangle
Label the triangle ABC
Measure the lengths of the triangle
Highlight the triangle and click ‘transform’ then ‘dilate’
Use a scale factor of ½
Make this triangle A’B’C’
Measure the Lengths of the new triangle
Move the triangle around examining what happensSlide48
GSP Questions
Is the new triangle a reduction or a enlargement?
What happens when you move triangle ABC?
If you dilate triangle A’B’C’ with the same scale factor what happens?
What Happens when you move the original triangle at the end of the steps above?Slide49
Bibliography
http://thewirecutter.com/reviews/best-tv-panasonic-st60/
spongebob.wikia.com
poohadventures.wikia.com
cartoons.wikia.com
mycrappyneighbor.com
en.wikifur.com
spongebob.neoseeker.com
www.mommypeach.com
spongebob.wikia.comSlide50
AnswersDilation Answers
Real Life applications answer – 300/15 = 20/11.25 cmEnlargementGSP AnswersWhen you move triangle ABC triangle A’B’C’ should move making the side lengths ½ triangle ABC
Reduction
The new triangle will have half the side lengths of triangle A’B’C’
A’B’C’ should be half the side length of Triangle ABC and The new triangle should be half the side lengths triangle A’B’C’Slide51
AnswersTranslation Answers
1: (x,y)>>>>(x+7,y+2) 2: <7,2>Reflection AnswersWhat is the equation of the line?
y=x-4
A(-1,-2) and B (8,-4), C (2,0). y= -2/9x+4/9
A (1,4), B (8,3), C (5,0). y= -
1/7x+5/7Slide52
AnswersRotation Answers
Vertices:A’ (4,10)B’ (5,8)C’ (5,6)D’ (3,6)
E’ (3,8)