transformations. there are four types –translations –reflections –rotation –dilation
TRANSCRIPT
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)