Transcript TODAY IN GEOMETRY…  Warm Up: WhiteBoards-Translations  Learning Target : 9.2 Given a pre-image, create an image by transformation by reflection  Independent Practice 

TODAY IN GEOMETRY…
 Warm Up: WhiteBoards-Translations
 Learning Target : 9.2 Given a pre-image,
create an image by transformation by
reflection
 Independent Practice
 AT: Ch.3 Test Corrections
WARM UP: Write a rule for the translation of the quadrilateral
𝐴𝐵𝐶𝐷 to quadrilateral 𝐴′𝐵′𝐶′𝐷′.
𝑃𝑜𝑖𝑛𝑡 𝐴: 𝐴 6, 2 → 𝐴′ −4, 7
𝐵′
𝐶′
𝐴′
𝐷′
𝐵
𝐶
𝐴
How did the quadrilateral move?
To the left 10 −10
Up 5 +5
𝐷
Right/Up = ADD
Left/Down = SUBTRACT
Rule: (𝒙, 𝒚) → (𝒙 − 𝟏𝟎, 𝒚 + 𝟓)
EXAMPLE: Graph △ 𝐴𝐵𝐶.
𝐴 7, 1 𝐵 3, 2 𝐶 5, −5
Reflect the pre-image across the line 𝑥 = 1.
EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF
REFLECTION
𝐵′
𝐴′
𝐵
𝐴
𝑃𝑜𝑖𝑛𝑡 𝐴: 7, 1 → −5, 1
𝑃𝑜𝑖𝑛𝑡 𝐵: 3, 2 → −1, 2
𝐶
𝐶′
𝑥=1
𝑃𝑜𝑖𝑛𝑡 𝐶: 5, −5 → −3, −5
EXAMPLE 2: Graph △ 𝐴𝐵𝐶.
𝐴 7, 1 𝐵 3, 2 𝐶 5, −5
Reflect the pre-image across the line 𝑥 = 5.
EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF
REFLECTION
𝑃𝑜𝑖𝑛𝑡 𝐴: 7, 1 → 3, 1
𝐵′
𝐵
𝐴′
𝐴
𝐶′ 𝐶
𝑥=5
𝑃𝑜𝑖𝑛𝑡 𝐵: 3, 2 → 7, 2
𝑃𝑜𝑖𝑛𝑡 𝐶: 5, −5 → 5, −5
PRACTICE: Graph △ 𝐴𝐵𝐶.
𝐴 3, 6 𝐵 −1, 7 𝐶 1, 0
Reflect the pre-image across the line 𝑦 = −1.
EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF
REFLECTION
𝐵
𝐴
𝑃𝑜𝑖𝑛𝑡 𝐴: 3, 6 → 3, −8
𝑃𝑜𝑖𝑛𝑡 𝐵: −1, 7 → −1, −9
𝐶
𝑃𝑜𝑖𝑛𝑡 𝐶: 1, 0 → 1, −2
𝐶′
𝑦 = −1
𝐵′
𝐴′
REFLECTION across the x-axis:
𝐴 −5, 5 → 𝐴′ −5, −5
𝐶 2, 7 → 𝐶 ′ 2, −7
𝐵 2, 7 → 𝐵′ 2, −7
𝐷 4, 2 → 𝐵′ 4, −2
𝐵
𝐴
The
distances
from the
mirror to
each point
is equal!
5
𝐶
𝐷
𝐷′
5
Notice that all xcoordinates of the preimage and image DOESN’T
change but the ycoordinates change signs!
RULE: (𝒙, 𝒚) → (𝒙, −𝒚)
𝐶′
𝐴′
𝐵′
Reflection
across the
x-axis so
the x-axis
is the
mirror
TRANSLATION/SLIDE:
TRANSFORMATION COORDINATE RULE
EXAMPLE
Translation (shift)
𝑥, 𝑦 → (𝑥 ± ℎ, 𝑦 ± 𝑘) (𝑥, 𝑦) → (𝑥 + 3, 𝑦 − 4)
Reflection across
𝑥 − 𝑎𝑥𝑖𝑠
Reflection across
𝑦 − 𝑎𝑥𝑖𝑠
Reflection across line
𝑦=𝑥
Reflection across line
𝑦 = −𝑥
90° counterclockwise
rotation
𝑥, 𝑦 → (𝑥, −𝑦)
180° rotation
𝑥, 𝑦 →
270° counterclockwise
rotation
𝑥, 𝑦 →
𝑥, 𝑦 →
𝑥, 𝑦 →
𝑥, 𝑦 →
𝑥, 𝑦 →
(4, 2) → (4, −2)
REFLECTION across the y-axis:
𝐴 −6, −3 → 𝐴′ 6, −3
𝐶 −2, −4 → 𝐶 ′ 2, −4
𝐵 −3, −1 → 𝐵′ 3, −1
𝐷 −5, −6 → 𝐵′ 5, −6
Notice that all ycoordinates of the preimage and image DOESN’T
change but the xcoordinates change signs!
RULE: (𝒙, 𝒚) → (−𝒙, 𝒚)
Reflection
across the
y-axis so
the y-axis
is the
mirror
The
distances
from the
mirror to
each point
is equal!
𝐵′
𝐵
𝐴
𝐷
3
3
𝐶
𝐶′
𝐴′
𝐷′
TRANSLATION/SLIDE:
TRANSFORMATION COORDINATE RULE
EXAMPLE
Translation (shift)
𝑥, 𝑦 → (𝑥 ± ℎ, 𝑦 ± 𝑘) (𝑥, 𝑦) → (𝑥 + 3, 𝑦 − 4)
Reflection across
𝑥 − 𝑎𝑥𝑖𝑠
Reflection across
𝑦 − 𝑎𝑥𝑖𝑠
Reflection across line
𝑦=𝑥
Reflection across line
𝑦 = −𝑥
90° counterclockwise
rotation
𝑥, 𝑦 → (𝑥, −𝑦)
(4, 2) → (4, −2)
𝑥, 𝑦 → (−𝑥, 𝑦)
(−3, −1) → (3, −1)
180° rotation
𝑥, 𝑦 →
270° counterclockwise
rotation
𝑥, 𝑦 →
𝑥, 𝑦 →
𝑥, 𝑦 →
𝑥, 𝑦 →
REFLECTION across line 𝒚 = 𝒙:
𝐴 −6, 5 → 𝐴′ 5, −6
𝐶 −2, 4 → 𝐶 ′ 4, −2
𝐵 −3, 7 → 𝐵′ 7, −3
𝐷 −5, 2 → 𝐵′ 2, −5
Notice that the x and y
coordinates switch values
from pre-image to image.
RULE: (𝒙, 𝒚) → (𝒚, 𝒙)
𝐵
𝐴
𝐶
𝐷
𝐶′
Reflection
across the
line 𝒚 = 𝒙
𝐷′
𝐵′
𝐴′
TRANSLATION/SLIDE:
TRANSFORMATION COORDINATE RULE
EXAMPLE
Translation (shift)
𝑥, 𝑦 → (𝑥 ± ℎ, 𝑦 ± 𝑘) (𝑥, 𝑦) → (𝑥 + 3, 𝑦 − 4)
Reflection across
𝑥 − 𝑎𝑥𝑖𝑠
Reflection across
𝑦 − 𝑎𝑥𝑖𝑠
Reflection across line
𝑦=𝑥
Reflection across line
𝑦 = −𝑥
90° counterclockwise
rotation
𝑥, 𝑦 → (𝑥, −𝑦)
(4, 2) → (4, −2)
𝑥, 𝑦 → (−𝑥, 𝑦)
(−3, −1) → (3, −1)
𝑥, 𝑦 → (𝑦, 𝑥)
(−5, 2) → (2, −5)
180° rotation
𝑥, 𝑦 →
270° counterclockwise
rotation
𝑥, 𝑦 →
𝑥, 𝑦 →
𝑥, 𝑦 →
REFLECTION across line 𝒚 = −𝒙:
𝐴 −5, −3 → 𝐴′ 3, 5
𝐶 −1, −4 → 𝐶 ′ 4, 1
𝐵 −2, −1 → 𝐵′ 1, 2
𝐷 −4, −6 → 𝐵′ 6, 4
Notice that the x and y
coordinates switch values
from pre-image to image.
RULE: (𝒙, 𝒚) → (−𝒚, −𝒙)
𝐴′
𝐵′
𝐵
𝐷′
𝐶′
𝐴
𝐶
𝐷
Reflection
across the
line 𝒚 = −𝒙
TRANSLATION/SLIDE:
TRANSFORMATION COORDINATE RULE
EXAMPLE
Translation (shift)
𝑥, 𝑦 → (𝑥 ± ℎ, 𝑦 ± 𝑘) (𝑥, 𝑦) → (𝑥 + 3, 𝑦 − 4)
Reflection across
𝑥 − 𝑎𝑥𝑖𝑠
Reflection across
𝑦 − 𝑎𝑥𝑖𝑠
Reflection across line
𝑦=𝑥
Reflection across line
𝑦 = −𝑥
90° counterclockwise
rotation
𝑥, 𝑦 → (𝑥, −𝑦)
(4, 2) → (4, −2)
𝑥, 𝑦 → (−𝑥, 𝑦)
(−3, −1) → (3, −1)
𝑥, 𝑦 → (𝑦, 𝑥)
(−5, 2) → (2, −5)
𝑥, 𝑦 → (−𝑦, −𝑥)
(−4, −6) → (6, 4)
180° rotation
𝑥, 𝑦 →
270° counterclockwise
rotation
𝑥, 𝑦 →
𝑥, 𝑦 →
PRACTICE: Graph △ 𝐴𝐵𝐶.
𝐴 3, 4 𝐵 −1, 5 𝐶 1, −2
Reflect the pre-image across the y-axis.
RULE FOR RELECTION ACROSS Y-AXIS: (𝑥, 𝑦) → (−𝑥, 𝑦)
𝐴′ 𝐵
𝐵′
𝐴
𝑃𝑜𝑖𝑛𝑡 𝐴: 3, 4 → −3, 4
𝐶′
𝐶
𝑃𝑜𝑖𝑛𝑡 𝐵: −1, 5 → 1, 5
𝑃𝑜𝑖𝑛𝑡 𝐶: 1, −2 → −1, −2
PRACTICE: Graph △ 𝐴𝐵𝐶.
𝐴 3, 4 𝐵 −1, 5 𝐶 1, −2
Reflect the pre-image across line 𝒚 = −𝒙.
RULE FOR RELECTION ACROSS LINE Y-AXIS: (𝑥, 𝑦) → (−𝑦, −𝑥)
𝐵
𝐴
𝐵′
𝐶′
𝐴′
𝐶
𝑃𝑜𝑖𝑛𝑡 𝐴: 3, 4 → −4, −3
𝑃𝑜𝑖𝑛𝑡 𝐵: −1, 5 → −5, 1
𝑃𝑜𝑖𝑛𝑡 𝐶: 1, −2 → 2, −1
𝒚 = −𝒙
HOMEWORK #2:
Pg. 593: 3-6, 8-10, 27-29
If finished, work on other assignments:
HW #1: Pg. 576: 3-14, 31