2.2 describing translations what is the relationship between a figure and its image under a...
TRANSCRIPT
2.2 Describing Translations
What is the relationship between a figure and its
image under a translation?As you work on each example, think
about the instructions you could give so that someone else could re-create the translation exactly.
A1) Draw a line segment from each vertex of polygon ABCDE
to its image.Diagram 1:
A
B
C
D
E
A1) Draw a line segment from each vertex of polygon ABCDE
to its image.Diagram 1:
P'1m DD' = 8.27 cm
m EE' = 8.25 cm
m AA' = 8.27 cm
m CC' = 8.24 cm
m BB' = 8.27 cm
A
B
C
D
E
B'
C'
D'
E'
A'
A2) Describe the relationship among the line segments you drew
A1) Draw a line segment from each vertex of polygon ABCDE
to its image.Diagram 1:
P'1m DD' = 8.27 cm
m EE' = 8.25 cm
m AA' = 8.27 cm
m CC' = 8.24 cm
m BB' = 8.27 cm
A
B
C
D
E
B'
C'
D'
E'
A'
A2) Describe the relationship among the line segments you drewThe
line segments are parallel to one
another and are the same
length.
A1) Draw a line segment from each vertex of polygon ABCDE
to its image.Diagram 2:
A
B
C
D
E
A2) Describe the relationship among the line segments you drew
A1) Draw a line segment from each vertex of polygon ABCDE to
its image.Diagram 2:
m AA' = 8.25 cm
m EE' = 8.26 cm
m DD' = 8.23 cm
m CC' = 8.24 cm
m BB' = 8.28 cm
AC
D
E
B
B'
C'
D'
E'
A'
A2) Describe the relationship among the line segments you drew
A1) Draw a line segment from each vertex of polygon ABCDE to
its image.Diagram 2:
m AA' = 8.25 cm
m EE' = 8.26 cm
m DD' = 8.23 cm
m CC' = 8.24 cm
m BB' = 8.28 cm
AC
D
E
B
B'
C'
D'
E'
A'
A2) Describe the relationship among the line segments you drew
The line
segments are parallel to one
another and are the same
length.
By performing the same translation that was used to slide polygon ABCDE to polygon A’B’C’D’E’, slide polygon A’B’C’D’E’ to create a new image. Label the new image
A”B”C”D”E”.
P'1m DD' = 8.27 cm
m EE' = 8.25 cm
m AA' = 8.27 cm
m CC' = 8.24 cm
m BB' = 8.27 cm
A
B
C
D
E
B'
C'
D'
E'
A'
By performing the same translation that was used to slide polygon ABCDE to polygon A’B’C’D’E’, slide polygon A’B’C’D’E’ to create a new image. Label the new image
A”B”C”D”E”.
P'1
B"
C"
D''
E''
A''
A
B
C
D
E
B'
C'
D'
E'
A'
By performing the same translation that was used to slide polygon ABCDE to polygon A’B’C’D’E’, slide polygon A’B’C’D’E’ to create a new image. Label the new image
A”B”C”D”E”.
P'1
B"
C"
D''
E''
A''
A
B
C
D
E
B'
C'
D'
E'
A'
Make sure the length of all of your line segments are the same!
By performing the same translation that was used to slide polygon ABCDE to polygon A’B’C’D’E’, slide polygon A’B’C’D’E’ to create a new image. Label the new image
A”B”C”D”E”.
m AA' = 8.25 cm
m EE' = 8.26 cm
m DD' = 8.23 cm
m CC' = 8.24 cm
m BB' = 8.28 cm
AC
D
E
B
B'
C'
D'
E'
A'
By performing the same translation that was used to slide polygon ABCDE to polygon A’B’C’D’E’, slide polygon A’B’C’D’E’ to create a new image. Label the new image
A”B”C”D”E”.
n' = 8.26 cm
m' = 8.23 cm
l' = 8.24 cm
k' = 8.28 cm
j' = 8.25 cm
k = 8.28 cm
j = 8.25 cm
n = 8.26 cm
m = 8.23 cm
l = 8.24 cm
AC
D
E
B
C'
D'
E'
A'
B'
By performing the same translation that was used to slide polygon ABCDE to polygon A’B’C’D’E’, slide polygon A’B’C’D’E’ to create a new image. Label the new image
A”B”C”D”E”.
n' = 8.26 cm
m' = 8.23 cm
l' = 8.24 cm
k' = 8.28 cm
j' = 8.25 cm
k = 8.28 cm
j = 8.25 cm
n = 8.26 cm
m = 8.23 cm
l = 8.24 cm
AC
D
E
B
C'
D'
E'
A'
B'
Make sure the length of all of your line segments are the same!
Polygon A”B”C”D”E” is the image of polygon ABCDE after two identical translations. How is the polygon A”B”C”D”E” related to polygon ABCDE?
Polygon A”B”C”D”E” is the image of polygon ABCDE after two identical translations. How is the polygon A”B”C”D”E” related to polygon ABCDE?
Book answer:
Polygon A”B”C”D”E” is twice as far from the original, in the same direction as polygon A’B’C’D’E’ is. The first images vertices are the midpoints of the line segments connecting an original vertex and its second image.
Does your final drawing have translational
symmetry? Explain.P'1
B"
C"
D''
E''
A''
A
B
C
D
E
B'
C'
D'
E'
A'
Does your final drawing have translational
symmetry? Explain.P'1
B"
C"
D''
E''
A''
A
B
C
D
E
B'
C'
D'
E'
A'
Book answer:
It is the beginning of translational symmetry. Technically, it does not have translational symmetry since the design does not repeat forever.
Bittner Answer: This design is a translation!
Complete the definition of a translation.A translation matches any two
points X & Y on a figure to image points X’ & Y’ so that… ______________________________ ________________________________________________________________________.
Complete the definition of a translation.A translation matches any two
points X & Y on a figure to image points X’ & Y’ so that… ______________________________ ________________________________________________________________________.
Key Points that need to be in your answer:
the distance between X & X’ is equal to the distance between Y & Y’.
the line XX’ is parallel to line YY’.
Bittner Bonus Question:A) If I only give you a shape, can you
perform a translation?
If yes, do it. If no, explain why not.
B) Can you perform the translation that I have in mind?
If yes, do it. If no, explain why not.A
B
CD
E
Bittner Bonus Question:If I only give you a shape, can you perform a
translation?
If yes, do it. If no, explain why not.
Can you perform the translation that I have in mind?
If yes, do it. If no, explain why not.A
B
CD
E
You could slide a duplicate image of the original object anywhere that you wanted to and that would be a translation. However, for you to do the translation that I wanted, I would have to tell you more information. I’d have to tell you the direction and distance I wanted you to use for the translation.
I will need to give you an ARROW to tell you the direction & the distance to slide it.
Bittner Bonus Question:For you to perform the translation that is
not on graph paper, you only need the original design and an arrow.
The arrow tells you the distance and direction to slide your image.
A
B
CD
E
Bittner Bonus Question:For you to perform the translation that is
not on graph paper, you only need the original design and an arrow.
The arrow tells you the distance and direction to slide your image.
A
B
CD
E