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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:
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”.
Characteristics and Tendencies:
• 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’ Non-
Examples: ABCD → A’C’B’D’
Transformations
A Foldable for your Journal
The Top FlapIII
III IV
(+,+)(-,+)
(-,-) (+,-)
X-Axis
Left and Right
- +
Y-Axis
Down and Up
- +
Coordinates(x,y)
Pre-Image → ImageA → A’Original → ResultBefore → 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 (pre-image) 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)
Reflection
The line you arereflecting over The item being
affected
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.
F
G
H
F’
H’
G’
On the Front of the Third PageFrom Pg 557 in Textbook
R y-axis (∆FGH)Reflection Figure Effected Axis of Reflection
Reflection (Flip)
F
G
H
F’
H’
G’
R y=-1 (∆FGH)
F
G
HF’
H’
G’
R y=x (∆FGH)(2,2
)
(4,-3)
(-2,-1)
(-1,-2)
(-3,4)
(2,2)
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 PageFrom Pg 565 in Textbook
r (90˚, O) (∆FGH)Figure Effected
Rotation Degree of Rotation
Center of Rotation (in
this case it is origin)
Rotation (Flip)
0˚=(x,y)90˚=(y,x)
180˚=(x,y)270˚=(y,x)360˚=(x,y)
Every Quadrant is a total of 90˚
F
J
H
F’
H’
G’
Quadrants
III
III IV
(+,+)
(-,+)
(-,-) (+,-)
Counter – ClockwisePositive Rotation
ClockwiseNegative Rotation
G
J’