Name___________________________________
Introduction to Transformations and Reflections
Date________________
Introduction to Transformations
Pair-Share: Answer the following questions with your partner.
1) What is a transformer?
2) Explain the different transformers that you have observed before.
3) What do transformers change into?
Watch the following Movie Trailer: https://www.youtube.com/watch?v=zaEWLuVJee0
Fill in the box below:
Original Transformers Movie
List of Transformations
(ex) Car Robot
Observations of Movie
Write a math definition of a transformation:
Vocabulary
A transformation is an operation that maps (or moves) a figure in the plane to a new
position.
The figure in its original position is called the preimage.
The figure in its new position after the transformation is called
the image. The five transformations that will be covered in this
unit are line reflections, translations, rotations, point reflections,
and dilations.
Pair-Share: There are 4 kinds of transformations. Can you list them?
1)
2)
3)
4)
*Look at the pictures below to brainstorm if you need a hint
Write the formal geometric term for each movement below:
n
A
A line reflection is a transformation in which a figure is reflected over a given
line. Each point of the preimage is the same distance from the line of reflection as
the corresponding point in the image. Thus, the line of reflection is the
perpendicular bisector of the segment that connects each preimage point to its
image point. In the diagram above, A ' B ' C ' is the image of ABC after a
reflection in line m. Line m is the perpendicular bisector of each line segment that
joins a preimage point to its corresponding image point. A line reflection is an opposite
isometry.
B
A figure has a line of symmetry if it is possible to draw a line through the figure so that each
half of the figure is a line reflection of the other half. In the diagram to the right, line n is a line
of symmetry in isosceles ABC .
Draw the line of symmetry, if possible for each example!
C
Reflections Discovery:
Part I 
1) Plot the points: D(4,2) R, (2, 2) E(3, 3), A(1, 6) and M(7,6)
2) Connect the points to create a pentagon
3) Reflect Pentagon DREAM over the x-axis
4) Write our new points below:
D’( , )
R’( , )
E’( , )
A’( , )
M’( , )
Write a rule: To reflect over the x-axis: (x, y)  (
Part 2 
1) Plot the points: L(2,2) U(4, 3) V(2, 6)
2) Connect the points to create a triangle
3) Reflect Triangle LUV over the y-axis
4) Write our new points below:
L’( , )
U’( , )
V’( , )
Write a rule:
To reflect over the y-axis: (x, y)  (
,
)
Part 3 
1) Draw the line y = x on your graph
2) Plot the points:
P(-1,-1)
I(-1, -4) G(4, -1)
3) Connect the points to create a triangle
4) Reflect Triangle PIG over the y=x line
5) Write our new points below:
P’( , )
I’( , )
G’( , )
Write a rule:
To reflect over the x=y line (x, y)  (
,
)
,
)
Practice:
(ex 1) Find the image of M(-4,2) A(-2, 2) T(-3, 3),
H(-1, 6) and Y(-7,6) after a reflection about the x-axis.
(ex 2) The vertices of quadrilateral BIRD are B(-1, -3), I(8, 0), R(3, 5), D(0, 4). Find the image
of these points after a reflection about the line y = x.
(ex 3) The vertices of quadrilateral ABCD are A (-7,3) B (-5,7) C (1,7) D (-1,3). Find the
image of these points after a reflection about the line y-axis.