Polygons and
Transformations
Unit 2
Essential Questions
1.) How can you change a figure’s position without
changing its size and shape?
2.) What process is used to perform a reflection
across a line?
What are Transformations? (Ch. 9.1)
Definition:
Characteristics and Tendencies:
The methodical movement of a geometric
figure on a plane. The starting figure is
called a “pre-image” and the resulting
figure is called an “image”.
• There are 4 types: Translation, Rotation,
Reflection, and Dilation.
• Follows the same naming/labeling rules
used with ≅ figures
• Translation, Rotation, and Reflection
•
are called the Rigid
•
Transformations.
Example:
∆ABC → ∆A’B’C’
Transformations
Non-Examples:
ABCD → A’C’B’D’
A Foldable for your Journal
X-Axis
Left and Right
The Top Flap
II
I
(-,+)
(+,+)
III
(-,-)
IV
(+,-)
-
+
Y-Axis
Down and Up
-
+
Coordinates
(x,y)
Pre-Image → Image
A → A’
Original → Result
Before → After
Problem 3 (pg 547)
T<-2,-5> (∆PQR)
Item Being
Affected
Translation
Change of X Value
Change of Y Value
Could Also be represented as:
(x-2, y-5)
Left 2 and Down 5
Inside the top flap
Summarize what is happening to the transformation in your own words!
What are Reflections? (Ch. 9.2)
•
•
•
•
•
•
A reflection over a line k is a transformation in which each point of the original figure (preimage) has an image that is the same distance from the line of reflection as the original
point but is on the opposite side of the line.
Remember that a reflection is a flip.
When reflecting over the x axis, the sign of y changes
When reflecting over the y axis, the sign of x changes
The notation for reflections: rk
The image keeps the same dimensions as the preimage
Lets take a look at an example
1.) Look at this problem and let’s go over it! (remember to put this cutout in
your journal, not in your foldable)
Ry-axis( ABC)
The line you are
reflecting over
The item being
affected
Reflection
X
Y
New X
New Y
A
-3
4
A’
3
4
B
0
1
B’
0
1
C
4
2
C’
-4
2
Since we’re reflecting over the y-axis,
only the X’s are affected
Now let’s go back to our foldable….
On the Inside of the 2nd flap
Summary:
Vertical or Horizontal Axis:
Count from each vertex of the pre-image to the axis of reflection and then
count the same value again.
y=x OR y=-x
Switch the x and y values for each vertex in the pre-image.
BOTH versions result in points that are equidistant from the axis of reflection.
On the Front of the Third Page
From Pg 557 in Textbook
R y-axis (∆FGH)
Reflection
R y=-1 (∆FGH)
R y=x (∆FGH)
Figure Effected
Axis of Reflection
G’
(2,2)
H’
G
G
(-3,4)
H’
F
H’
F’
F’
G
G’
(2,2)
(-2,-1)
F
F
H
H
G’
Reflection (Flip)
F’
(-1,-2)
(4,-3)
H
Inside the top flap
Summarize in your own words how to reflect an object!
Now Let’s Practice!
On the Back of the Third Page
Summary:
Based on the required rotation to each
vertex, determine the resulting Quadrant,
switch the x and y values if necessary, and
then apply the – and + values as
appropriate.
On the Front of the Fourth Page
From Pg 565 in Textbook
Quadrants
II
(-,+)
III
(-,-)
I
(+,+)
IV
(+,-)
0˚=(x,y)
90˚=(y,x)
180˚=(x,y)
270˚=(y,x)
360˚=(x,y)
r (90˚, O) (∆FGH)
Figure Effected
Rotation
Degree of Rotation
Center of Rotation (in
this case it is origin)
J’
F
J
G
H’
F’
Counter – Clockwise
Positive Rotation
Every Quadrant
is a total of 90˚
Clockwise
Negative Rotation
Rotation (Flip)
G’
H