coordinate reflections - 2
DESCRIPTION
Coordinate Reflections - 2. Reflecting over the y = x and y = -x lines. Homework: Reflections on the Coordinate Plane WS 2. UPDATE: Reflection Notation . The line y=x. Where the x and y coordinates are equal: (1,1), (5,5), (-3, -3)…. (2, 2). (-1, -1). (-5, -5). - PowerPoint PPT PresentationTRANSCRIPT
Coordinate Reflections - 2Reflecting over the
y = x and y = -x lines
Homework: Reflections on the Coordinate Plane WS 2
Reflection in the x-axis:
Reflection in the y-axis:
𝑟 𝑥−𝑎𝑥𝑖𝑠∆ 𝐴𝐵𝐶
𝑟 𝑦−𝑎𝑥𝑖𝑠∆ 𝑋𝑌𝑍
UPDATE: Reflection Notation
The line y=xWhere the x and y coordinates are equal:
(1,1), (5,5), (-3, -3)…
(2, 2)
(-5, -5)(-1, -1)
Reflect across y = x
x,y y,xSwap x and y
Notation:
Rule:
Name the coordinates of the original object:
NI
WW: (9, 8)
I: (9, 3)
N: (1, 1)
I’ W’
N’Name the coordinates of the reflected object:
W’: (8, 9)
I’: (3, 9)
N’: (1, 1)
A point ON the line of
reflection is its own reflection
𝑟 ( 𝑦=𝑥 )∆𝑊𝐼𝑁
A(1, 2) A'(2, 1)
B(3, 5) B'(5, 3)
C(4, –3) C'(–3, 4)
D(2, –5) D'(–5, 2) A'
B'
C'
D'
𝑟 ( 𝑦=𝑥 )𝐴𝐵𝐶𝐷
The line y = -xWhere the x and y coordinates are opposites:
(1,-1), (-5,5), (3, -3)…
(-2, 2)
(4, -4)
Reflect across y = -x
x,y y, x Swap and change both signs
𝑁𝑜𝑡𝑎𝑡𝑖𝑜𝑛 :𝑟 (𝑦=−𝑥)
Rule:
Name the coordinates of the original object:
A: (-4, 6)
B: (-1, 6)
C: (-1, 3)
Name the coordinates of the reflected object:
A’: (-6, 4)
B’: (-6, 1)
C’: (-3, 1)
A’
B’ C’
𝑟 ( 𝑦=−𝑥)∆ 𝐴𝐵𝐶
𝑟 ( 𝑦=−𝑥)∆ 𝐴𝐵𝐶
Name the coordinates of the original object:
A: (1,2)
B: (1,5)
C: (3,2)Name the coordinates of the reflected object:
A’: (-2,-1)
B’: (-5, -1)
C’: (-2, -3)
C’
B’ A’
Reflection in y = x:
Reflection in y = -x:
Reflection Notation
𝑟 ( 𝑦=−𝑥)∆ 𝐴𝐵𝐶
𝑟 ( 𝑦=𝑥 )∆𝑋𝑌𝑍
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
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)
D’
R’
P’
UName the coordinates of the
reflected object:R’’: (9, -9)
P’’: (8, -5)
D’’: (2, -4)
U’’: (9, -2)
How were the coordinates affected when the object was reflected over both the x-axis and y-axis?
U’
D’’P’’
U’’
R’’
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.
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 180°?
Think About It