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Transcript of Translations
Translations
Unit 2 Section 1
What is a translation?
• Moving a shape, without rotating or flipping it. "Sliding". The shape still looks exactly the same, just in a different place.
Example 1.) Use the translation
What is the image of ?
( , ) ( 2, 5)x y x y
( 3,6)A
Practice 1.) Use the translation
What is the image of ?
( , ) ( 3, 4)x y x y
(4, 2)B
Example 2.) Use the translation
What is the preimage of ?
( , ) ( 1, 2)x y x y
'(4, 1)C
Practice 2.) Use the translation
What is the preimage of ?
( , ) ( 3, 5)x y x y
'(4, 6)D
Example 3.) The vertices of
Graph the image of the triangle using prime notation.
( 2,3), (4, 1), ( 3, 2)ABC are A B C
( , ) ( 5, 1)x y x y
Practice 3.) The vertices of
Graph the image of the triangle using prime notation.
( 2,3), (4, 1), ( 3, 2)ABC are A B C
( , ) ( 2, 3)x y x y
Example 4.)
Write a rule for the translation.
' ' ' .A B C is theimageof ABC after a translation
( 2, 1), ( 3,2), (4,2)
'(4, 2), ' 3,1 , '(10,1)
A B C
A B C
Practice 4.)
Write a rule for the translation.
' ' ' .A B C is theimageof ABC after a translation
(3, 1), ( 2,2), (0, 3)
'(0,1), ' 5, 4 , '( 3, 1)
A B C
A B C
Vectors
F
G
Horizontal component (5 units right)
Vertical Component(3 units up)
Initial Point
The component form of a vector combines the horizontal and vertical components. So, the component form of is 5,3FG
��������������
Example 5.) Name the vector and write its component form
A
B
M
N
Practice 5.) Name the vector and write its component form
E
F
Example 6.) The vertices of
Translate the triangle using the vector
(2, 1), ( 2, 4), (3, 5)ABC are A B C 2,4
Practice 6.) The vertices of
Translate the triangle using the vector
( 3, 2), (1, 5), (2,6)ABC are A B C 3, 1
Example 7.) Use the point A(-2,5). Find the component form of the vector that
describes the translation to P’.
A.) P’(3,-2)B.) P’(-4,5)C.) P’(2,4)D.) P’(-1,-6)