Transformations. There are four types –Translations –Reflections –Rotation –Dilation.

Transformations

There are four types

– Translations– Reflections– Rotation– Dilation

Vocabulary

• Congruent – Size and shape are exactly the same

• Similar – Shape is the same, but size is different.

• Proportional – Lengths change at the same rate or scale.

Translation

• Size and shape do not change. Only the location– SLIDE

Notation

• When transforming a shape, each new point is marked with ‘

– A’ means “A prime”– B’ means “B prime”

What did we do to it to get to the new location?

A

A’ Right 2, Up 5

What did we do to it to get to the new location?

A

A’

Left 4, Down 4

Translating Shapes

• When translating shapes, translate each point.

A

B C

'A

'B 'C

Which figure did we start with?What did we do to it to get to the new location?

38

Right 8, Up 3

A

B C

D

'C'B

'A 'D

• Which coordinate controls left and right movement? (x, )

You can describe left and right movement as addition or subtraction to x.

• Example: a translation of 4 units right could be described as (x + 4, y)

• The second coordinate (y) controls up and down movement. ( , y)

• You can describe up and down movement as addition or subtraction to y.

• Example: a translation of 4 units up could be described as (x, y + 4)

Writing New Coordinates

• Moving left or right affects x right is + Left is –

• Moving up or down affects y up is + down is –

A

'A

Describe the translation in terms of x and y

Example

• The point moves right 3 up 4 from the initial point (2, 3)

( , ) (3 ' )4 , 'x xy y

( , ) (3 5'4 )7 ',yx 2 3

A

'A

A

'A

A

'A

Describe the translation

(3, 5)

(6, 5)

(3, 8)

(5, 9)’

(8, 9)’

(5, 12)’

(x + 2, y + 4)

Describe the translation

(-7, 2)

(-9, -3)

(-5, 6)

(-2, -1)’

(-4, 0)’

(0, 3)’

Closure

• What is a good word to describe translation?

Closure

• Is the resulting shape of a translation similar or congruent?

A

'A

Closure: Describe the translation in terms of (x, y)