Download - Coordinate Reflections - 2
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Coordinate Reflections - 2Reflecting over the
y = x and y = -x lines
Homework: Reflections on the Coordinate Plane WS 2
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Reflection in the x-axis:
Reflection in the y-axis:
π π₯βππ₯ππ β π΄π΅πΆ
π π¦βππ₯ππ β πππ
UPDATE: Reflection Notation
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The line y=xWhere the x and y coordinates are equal:
(1,1), (5,5), (-3, -3)β¦
(2, 2)
(-5, -5)(-1, -1)
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Reflect across y = x
x,y y,xSwap x and y
Notation:
Rule:
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Name the coordinates of the original object:
NI
WW: (9, 8)
I: (9, 3)
N: (1, 1)
Iβ Wβ
NβName the coordinates of the reflected object:
Wβ: (8, 9)
Iβ: (3, 9)
Nβ: (1, 1)
A point ON the line of
reflection is its own reflection
π ( π¦=π₯ )βππΌπ
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A(1, 2) A'(2, 1)
B(3, 5) B'(5, 3)
C(4, β3) C'(β3, 4)
D(2, β5) D'(β5, 2) A'
B'
C'
D'
π ( π¦=π₯ )π΄π΅πΆπ·
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The line y = -xWhere the x and y coordinates are opposites:
(1,-1), (-5,5), (3, -3)β¦
(-2, 2)
(4, -4)
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Reflect across y = -x
x,y y, x Swap and change both signs
πππ‘ππ‘πππ :π (π¦=βπ₯)
Rule:
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Name the coordinates of the original object:
A: (-4, 6)
B: (-1, 6)
C: (-1, 3)
Name the coordinates of the reflected object:
Aβ: (-6, 4)
Bβ: (-6, 1)
Cβ: (-3, 1)
Aβ
Bβ Cβ
π ( π¦=βπ₯)β π΄π΅πΆ
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π ( π¦=βπ₯)β π΄π΅πΆ
Name the coordinates of the original object:
A: (1,2)
B: (1,5)
C: (3,2)Name the coordinates of the reflected object:
Aβ: (-2,-1)
Bβ: (-5, -1)
Cβ: (-2, -3)
Cβ
Bβ Aβ
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Reflection in y = x:
Reflection in y = -x:
Reflection Notation
π ( π¦=βπ₯)β π΄π΅πΆ
π ( π¦=π₯ )βπππ
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x-axis x,y x, y
x,y x,y y-axis x,y y,xy = x
y = -x x,y y, x
Rules of REFLECTION
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Reflect the object below over the x-axis and then the y-axis:Name the coordinates of the
original object: R
PD
R: (-9, 9)
P: (-8, 5)
D: (-2, 4)
U: (-9, 2)
Dβ
Rβ
Pβ
UName the coordinates of the
reflected object:Rββ: (9, -9)
Pββ: (8, -5)
Dββ: (2, -4)
Uββ: (9, -2)
How were the coordinates affected when the object was reflected over both the x-axis and y-axis?
Uβ
DββPββ
Uββ
Rββ
Would it make a difference if we
reflected over the y-axis first and then the x-axis? Try it! Then
reflect about what you discovered.
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How were the coordinates affected when the object
was reflected over both the x-axis and y-axis?
Would it make a difference if we
reflected over the y-axis first and then the x-axis? Try it! Then reflect about
what you discovered.
Would the result of this double reflection be the same as a rotation of the original
figure of 180Β°?
Think About It