today in geometry… warm up: whiteboards-translations learning target : 9.2 given a pre-image,...
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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 to quadrilateral .
𝐴𝐵
𝐶 𝐷
𝐴 ′𝐵 ′
𝐶 ′ 𝐷 ′
How did the quadrilateral move?To the left 10 Up 5
Right/Up = ADDLeft/Down = SUBTRACT
Rule:
EXAMPLE: Graph . Reflect the pre-image across the line .EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF REFLECTION
𝐴𝐵
𝐶
𝐴 ′ 𝐵 ′
𝐶 ′
𝑥=1
EXAMPLE 2: Graph . Reflect the pre-image across the line .EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF REFLECTION
𝐴
𝐵
𝐶
𝐴 ′𝐵 ′
𝐶 ′
𝑥=5
PRACTICE: Graph . Reflect the pre-image across the line .EACH POINT IN A REFLECTION IS EQUAL DISTANT FROM THE LINE OF REFLECTION
𝐴𝐵
𝐶
𝐴 ′𝐵 ′
𝐶 ′𝑦=−1
REFLECTION across the x-axis:
𝐴𝐵
𝐶𝐷
Reflection across the x-axis so the x-axis is the mirror
5
5
𝐴 ′
𝐷′
𝐵′
𝐶 ′
Notice that all x-coordinates of the pre-image and image DOESN’T change but the y-coordinates change signs!RULE:
The distances from the mirror to each point is equal!
TRANSLATION/SLIDE:TRANSFORMATION COORDINATE RULE EXAMPLE
Translation (shift)
Reflection across
Reflection across
Reflection across line
Reflection across line
counterclockwise rotation
rotation
counterclockwise rotation
(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)
(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)
REFLECTION across the y-axis:
𝐴𝐵
𝐶𝐷
Reflection across the y-axis so the y-axis is the mirror
33𝐵′
𝐶 ′𝐷′
𝐴′
Notice that all y-coordinates of the pre-image and image DOESN’T change but the x-coordinates change signs!RULE:
The distances from the mirror to each point is equal!
TRANSLATION/SLIDE:TRANSFORMATION COORDINATE RULE EXAMPLE
Translation (shift)
Reflection across
Reflection across
Reflection across line
Reflection across line
counterclockwise rotation
rotation
counterclockwise rotation
(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)
(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)
(−𝑥 , 𝑦 ) (−3 ,−1) →(3 ,−1)
REFLECTION across line :
𝐴𝐵
𝐶𝐷
Reflection across the line
𝐵′𝐶 ′
𝐷′
𝐴′
Notice that the x and y coordinates switch values from pre-image to image.RULE:
TRANSLATION/SLIDE:TRANSFORMATION COORDINATE RULE EXAMPLE
Translation (shift)
Reflection across
Reflection across
Reflection across line
Reflection across line
counterclockwise rotation
rotation
counterclockwise rotation
(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)
(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)
(−𝑥 , 𝑦 ) (−3 ,−1) →(3 ,−1)
(𝑦 ,𝑥) (−5 ,2) →(2 ,−5)
REFLECTION across line :
𝐴𝐵
𝐶𝐷
Reflection across the line
𝐷′𝐴 ′
𝐵′
𝐶 ′
Notice that the x and y coordinates switch values from pre-image to image.RULE:
TRANSLATION/SLIDE:TRANSFORMATION COORDINATE RULE EXAMPLE
Translation (shift)
Reflection across
Reflection across
Reflection across line
Reflection across line
counterclockwise rotation
rotation
counterclockwise rotation
(𝑥±h , 𝑦 ±𝑘)(𝑥 , 𝑦 )→(𝑥+3 , 𝑦−4)
(𝑥 ,− 𝑦 ) (4 ,2)→(4 ,−2)
(−𝑥 , 𝑦 ) (−3 ,−1) →(3 ,−1)
(𝑦 ,𝑥) (−5 ,2) →(2 ,−5)
(− 𝑦 ,− 𝑥) (−4 ,−6) →(6 ,4)
PRACTICE: Graph . Reflect the pre-image across the y-axis.
RULE FOR RELECTION ACROSS Y-AXIS:
𝐴𝐵
𝐶
𝐴 ′ 𝐵 ′
𝐶 ′
PRACTICE: Graph . Reflect the pre-image across line .
RULE FOR RELECTION ACROSS LINE Y-AXIS:
𝐴𝐵
𝐶𝐴 ′
𝐵 ′
𝐶 ′
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