Cartoon Transformations. By : Justin Fernandez, Fiona McClean , Sebastian Quiana , Eric Spiniello , and Wendy Star. Rotations – Fiona McClean Looney Tunes Reflections – Wendy Starr Simpsons Translations – Eric Spiniello Tom and Jerry Tessellations – Justin Fernandez Scooby Doo
By: Justin Fernandez, Fiona McClean,
Sebastian Quiana, Eric Spiniello, and Wendy Star
By: Fiona McClean
A rotation is an isometry where shapes rotate around a fixed point in a circular motion, whether clockwise or counter clockwise
Angle of Rotation:
A (-4,4,) A’ (4,4)
B (-2,4) B’ (4,2)
C (-2,2) C’ (2,2)
D (-4,2) D’ (2,4)
Center of Rotation:
Angle of Rotation:
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’.
A (16.5, 7)
B (14, 6.5)
C (12.5, 7)
D (13, 9)
E (14.5, 9.5)
The top of Tweety’s bird cage has rotational symmetry. It can be mapped onto itself at 36 degrees.
"Looney Tunes." SAT 400. N.p., n.d. Web. 23 Apr. 2013. <http://www.sat400.com/ satlooney.html>.
In a regular polygon, the number of lines of symmetry is equal to the number of side.
2 LinesLine of Symmetry
In a non regular polygon, one must just count.
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 ReflectionEquation Line of Reflection
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.
C (4,0)Minimum Distance
What is the equation of the line A’B?
If a character from the Simpsons were to look into a mirror they would see their face reflected back at them.Real Life Application
Slide 1: http://images1.wikia.nocookie.net/__cb20100602025911/simpsons/images/6/65/Bart_Simpson.png
Chapter 7 Resource Book Lesson 7.2Bibliography
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.
In 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).Mammy Two Shoes Mathematical Examples
You 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]
If 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).
In cartoons, translations are everywhere. For example, as Tom runs after Jerry, both characters are translating and moving across the screen.Real World Applications
A tessellation is the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps
In this case four 90 degree anglesWhat's a TesserrationRaggy?
The tessellation made in this floor tilling is made of regular squares alternating from white to blackJeepers Gang, look at that Tessellation!
Find a picture that you want to tessellate like this one. A square, rectangle, right triangle, or regular triangle would be the easiest.
paper size which is selected when
you select File New then in the
Present drop down menu select U.S.
PaperHow to Create a Scooby Snack (Tessellation)
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 duplicate
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 image
12. Keep doing this until the whole page is filled. The final project should look somewhat like this.
Dilation – Transformation that produces a shape that is different in size
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.
300 cmReal Life Application