Slide 1

Today – Wednesday, April 24 2013
 Checking for completion of Reflection
Discovery WS
 Warm Up: EOC Practice #5

 Learning Target : Given a pre-image, create
an image by transformation by reflection or
rotation
 Independent Practice


Slide 2

WARM UP (15 minutes):
EOC PRACTICE #5
We will check answers as a class.


Slide 3

CHECKING FOR COMPLETION:
REFLECTION DISCOVERY
WORKSHEET
Take this worksheet out so I can
check it!


Slide 4

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


Slide 5

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′


Slide 6

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′


Slide 7

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


Slide 8

REFLECTION:

(−5, 5) → (2, 5)
𝑥−𝑦
−𝑥 𝑦

(−5, 5) → (−5, −5)
(−5, 5) → (5, 5)

(𝑥, 𝑦) → (𝑦, 𝑥)

(−5, 5) → (5, −5)

(𝑥, 𝑦) → (−𝑦, −𝑥)

(−5, 5) → (−5, 5)


Slide 9

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


Slide 10

PRACTICE: Graph △ 𝐴𝐵𝐶.
𝐴 3, 4 𝐵 −1, 5 𝐶 1, −2
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


Slide 11

In Class HW #2:
9.3 Reflection worksheet

20 minutes then you will turn it in
then we are moving on to rotation.


Slide 12

INDEPENDENT WORK
(20 minutes):
ROTATION DISCOVERY
WORKSHEET


Slide 13

Notice that all x𝟗𝟎° CLOCKWISE ROTATION:

coordinates
of the pre′
𝐵 2, 7 image
→ 𝐵 and
2, −7
image DOESN’T
′
𝐷 4, 2 change
→ 𝐵 but
4, −2
the ycoordinates change signs!
RULE: (𝒙, 𝒚) → (𝒙, −𝒚)

′

𝐴 −5, 5 → 𝐴 −5, −5
𝐶 2, 7 → 𝐶 ′ 2, −7

𝐶′

𝐵′

𝐵

𝐷′

𝐴
𝐴′

𝐶
𝐷
Reflection
about the
point A


Slide 14

ROTATION:

(−5, 5) → (2, 5)
𝑥−𝑦
−𝑥 𝑦

(−5, 5) → (−5, −5)
(−5, 5) → (5, 5)

(𝑥, 𝑦) → (𝑦, 𝑥)

(−5, 5) → (5, −5)

(𝑥, 𝑦) → (−𝑦, −𝑥)

(−5, 5) → (−5, 5)

(𝑥, 𝑦) → (−𝑦, 𝑥)

(−5, 5) → (−5, −5)

(𝑥, 𝑦) → (−𝑥, −𝑦)

(−5, 5) → (5, −5)

(𝑥, 𝑦) → (𝑦, −𝑥)


Slide 15

HOMEWORK #2:
9.3 Reflection Worksheet
If finished, work on other assignments:
HW #1: Pg. 576: 3-14, 31