Transformations in Baseball
Nick Miller
Jeen Kim
Mary Ham
Amar Thakkar
Inning 6
Main Menu
Dilations by Nick Miller
Rotations by Jeen Kim
Reflections by Mary Ham
Translations by Amar Thakkar
Tessellation by Group
Dilations
By Nicholas Miller
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Dilation
Scale Factor
What is the Scale Factor?
Matrices
New Image and Preimage
Theorem
Problems
Dilations for Baseball
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Dilation
• Dilation is a similarity transformation in which
a figure is enlarged or reduced using a scale
factor ≠ 0, without altering the center
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Scale Factor
• The amount by which an object enlarges or
reduces is known as the scale factor
• If the scale factor is a number of a fraction
larger than 1, the new figure is an
enlargement of the pre image
• If the scale factor is a number or a fraction less
than one, than the new figure is a reduction of
the pre image
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What is the Scale Factor?
To find the scale factor, put the B’
coordinates over the pre image B
coordinates:
-2/-1 for x
6/3 for y
They should both come out to the
same thing
In this case, the scale factor is 2
If you are given the scale factor in a
problem, and you need to find out
the coordinates either the pre
image or the new figure, either
multiply or divide the coordinates
of the figure you already have, and
you get the new coordinates
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Matrices
What you see in the top left
corner of the picture is called
a matrices, which gives people
a better organization of
finding the new coordinates
In the photo, 2 is the scale
factor, and you have the
coordinates of the preimage
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New Image and Preimage
• In a dilation, the new image created from the
preimage is similar to the preimage.
• The figures would be congruent only if the
scale factor is 1
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• If B is not the center
point O, then the
image point P’ lies
on line CB
• The scale factor k is
a positive number
such that k= OB’/OB
and K doesn’t = 1
• If B is the center
point O, then B=B
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Theorem
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What are the new coordinates if the
scale factor is 3?
A--- (1,1)
1x3=3
1x3=3
B--- (2,3)
2x3=6
3x3=9
C--- (4,1)
4 x 3 = 12
1x3=3
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A= (3,3)
B= (6,9)
C= (12,3)
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B= (-2,4)
D= (1,1)
A= (-5,1)
C= (-2,3)
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What are the
coordinates
of the
baseball field
if the scale
factor is 1/3
with the
center point
(-2,0)
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• In baseball, the field is a
diamond. An example
using the baseball
diamond is if a little league
field wanted to be
renovated, and be made
bigger, the dilation would
be an enlargement from
the little league size field
to the middle school size
field.
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Dilations for Baseball
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Rotations
By Jeen Kim
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Rotation Table of Contents
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Rotation
Vocabulary/Key Concepts
Things to Know
Examples
Real Life Applications
Activity
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Rotation
• Rotation:
o A transformation where a figure is turned around
a center of rotation.
o A rotation is an isometry (a transformation where
the figure stays congruent)
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Vocabulary/Key Concepts
• Center of Rotation:
o A fixed point anywhere that the figure rotates about
• Angle of Rotation:
o The angle created by rays drawn from the center of rotation to a
point and its image.
• Theorem:
o Line K and line M intersect at point P. Then a reflection in line K
and the line M is a rotation about point P.
o The angle of rotation is double the angle formed by K and M.
• Rotational Symmetry:
o A figure in the plane has rotational symmetry if the figure can
be mapped onto itself by clockwise rotation of 180 degrees or
less.
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Things to Know
• Angle of Rotation:
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R90° (x,y) = (-y, x)
R180° (x,y) = (-x,-y)
R270° (x,y) = (y,-x)
R-90° (x,y) = (y,-x)
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Examples
• Rotational Symmetry
180°
Before:
After:
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Real Life Applications
• Rotations can be found in Baseball!
• From the pitching mound to the bases, the
base runner is the object that rotates and the
pitcher is the center of rotation.
The batter ran from the home
plate to second base, which is
a rotation of 180°.
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Rotation Activity
Rotate the shape by 60° CLOCKWISE.
TIP: Use a protractor and a ruler.
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Rotation Activity
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Find the angle of rotation
Draw the shape from the origin if the angle
of rotation is 120°
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Find the angle of rotation
Draw the shape from the origin if the angle
of rotation is 120°
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Reflections
By Mary Ham
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Key Words
What is a Reflection?
Reflection
How to Reflect Pre-images
Determine Lines of Symmetry
How to Find Line of Symmetry
Line of Symmetry in Baseball
Reflect Your Own Baseball! 
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Key Words
• Line of reflection- A
line that acts like a
mirror in a
reflection.
• Line of symmetryAn imaginary line
that you could fold
the image and both
halves match
exactly.
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Line of Reflection
Rectangle has 2 lines of Symmetry
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What is reflection??
• Reflection is a transformation which uses a
line that acts like a mirror, with an image
reflected in the line.
• Reflection is an isometry.
– Isometry is a transformation that preserves
lengths.
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Reflection
• If a figure is reflected over the y-axis, then
the y value stays the same but x value
becomes opposite and vice versa.
If the line of reflection is yaxis, then the y value stay the
same and x value become
opposite.
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How to reflect pre-images
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Use the following equation:
Rx-axis (x,y)=(x,-y)
Ry-axis (x,y)=(-x,y)
Ry=x (x,y)= (y,x)
Ry=-x (x,y)= (-y,-x)
Or
1. Draw the perpendicular line of the line of
reflection from a point.
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How to reflect pre-images (Cont)
2. Draw the point in the different side of line of
reflection; the distance from the image and line
of reflection has to be the same distance from
the pre-image from the line reflection.
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Determine Lines of Symmetry
• There’s not really a way to find lines of
symmetry by equation.
• However, if a figure is a regular polygon, then
the number of sides is equal to the number
of lines of symmetry.
Square
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# of sides: 4
# of lines of symmetry:4
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How to find line of reflection
• 1. Find pairs of reflecting (corresponding)
points.
• 2. Find the midpoint of the pair of reflecting
points.
• 3. Connect the midpoints; the line has to be a
straight line.
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Line of Symmetry in Baseball
A base ball and a baseball field have one line of symmetry
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Reflect your own baseball 
• Stuff you need:
Graph paper or
coordinate grid,
pencil, eraser,
and Computer
if using GSP
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1. Draw a pre-image of
a baseball that you
would like to reflect
on the coordinate
grid.
2. Draw the line of
reflection where you
want to reflect the
baseball.
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Make your own reflection (Cont.)
3. Reflect the pre-image over the line of
reflection, the shape has to be exact.
4. Then you got yourself a reflection 
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Translations
By Amar Thakkar
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Summary
Vocabulary
Example
Solution
Real World Examples
GSP Activity
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Summary
• Translations are basically the sliding of a shape
from one section to another section. On a grid
you can find a translated figure if you have a
coordinate notation or component form or
you can find these by calculating the distance
traveled x and y or y and x to find the
coordinate notation or component form.
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Vocabulary
• A translation is a transformation that maps
every two points P and A in the plane to
points P’ and Q’, so that the following
properties are true:
PP’ = QQ’ and 2)’ ll ’, or and’ are collinear.
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Vocabulary
• A vector is a quantity that has both direction
and magnitude, or size.
• When a vector is drawn , the initial point, or
starting point, of the vector is drawn point P
and the terminal point, or ending point, of
the vector is point Q. is read “vector PQ”
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Vocabulary
• The component form of a vector combines
the horizontal and vertical components
Component Form Ta,b(x,y)= (x+a) (y+b)
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EXAMPLE
• Find the coordinate
notation and
component form of this
translation.
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Solution
• Coordinate Notation
(x-5, y+3)
• Component Form
<-5, 3>
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Real world Examples
• When a runner runs
around the bases each
time he or she reaches
a new base, a
translation of 60 units
has happened.
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GSP Activity
• Click on Graph show grid
• Draw three points on the grid and connect
them with line segments
• Select all three sides with the cursor and copy
the triangle by pressing control c
• Go to another section of the grid and press
control v to paste
• Find the coordinate notation and component
form.
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Tessellation
By Group
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Tessellation by Nick Miller
Vocabulary/Key Terms by Mary Ham
Real Life Examples by Amar Thakkar
Activity by Jeen Kim
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What is a Tessellation?
• A tessellation is a repeating pattern of figures
that completely covers a plane without any
gaps or overlaps
• To tessellate is to cover a plane surface by
repeated use of a single shape, without any
gaps or overlapping
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Key Terms
• Tessellation- A repeating
pattern of figures that
completely covers a plane
without any gaps or overlaps.
• Edge- Intersection between
two bordering tiles.
• Vertex- Intersection of three
or more bordering tiles.
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Key Terms (cont)
• Regular Tessellation- When a tessellation uses
only one type of regular polygon to fill up a
plane.
• Semi-regular Tessellation- When a tessellation
uses more than one type of regular polygon to
fill up a plane.
Regular tessellation
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Semi-regular tessellation
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Real-Life Example
• 4 random bases joined
together form a
tessellation.
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• Use 4 regular hexagons and 6 regular triangles to create a
tessellation.
Tessellation Activity
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Tessellation Activity
• Example Answer:
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LAST INNING
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Design and Editing by: Jeen Kim
Dilations by: Nick Miller
Rotations by: Jeen Kim
Reflections by: Mary Ham
Translations by: Amar Thakkar
Reflections by: the Group
Rotation Bibliography
http://www.regentsprep.org/Regents/math/g
eometry/GT4/ROTATEPIC3.gif
Clip Art on Microsoft PowerPoint
Blank Coordinate Plane from Mrs. Haemmerle
McDougal Littell Inc. Geometry Chapter 7
Resource Book
Reflection Bibliography
Images
Baseball 1:http://www.sullivanil.us/SYB.html
Coordinate:
http://www.regentsprep.org/Regents/math/ALGE
BRA/MultipleChoiceReview/Shapes.html
Baseball 2:http://mypixelpress.com/photobaseball-red-thread-63.html
Baseball field:
http://www.topendsports.com/image/clipart/bas
eball/baseball-diamond-field.gif.php
Tessellation Bibliography
Clip Art on Microsoft Powerpoint
GIFs/JPEGs
http://www.beechmontyouthsports.com/images
/baseball_player__runningA.gif
http://www.fangraphs.com/blogs/wpcontent/uploads/2013/04/Rutledge.gif.opt_.gif
http://www.fangraphs.com/blogs/wpcontent/uploads/2013/02/Berry2B.gif.opt_.gif
http://2.bp.blogspot.com/SzlHhVj3i0o/UQ_E52pAMaI/AAAAAAAADZs/v3FVFHcNCY/s1600/image1.jpg