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

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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)