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Composite Transformations
Contributed by: Miles
(Original author: Dilaura)
A composition of transformations is...
musical isometry
written transformations
two or more transformations
a movie about transformations
A glide reflection is shown below.
A glide reflection is...
a rotation + a translation
a reflection + a translation
a reflection + a rotation
two reflections
An isometry is a transformation in which the original figure and its image are congruent.
Examples of "rigid transformations" include translations, reflections, and rotations.
True or False:
A composition of two rigid transformations is an isometry.
True
False
A composition of two reflections across 
two parallel lines is equal to:
a reflection
a rotation
a translation
a dilation
A composition of two reflections overintersecting lines is equivalent to...
a reflection
a rotation
a translation
a dilation
Which composite transformation maps ∆ABC onto ∆A''B''C''
 T<8, -2> ○ R180º
T<14, 3> ○ T<-6, -5>
T<14, 3> ○ ry-axis
T<14, 3> ○ >T><8, -2>
∆ABC undergoes ry-axis, then  T(x,y) → (x, y-3)
Find the coordinates of A' and A''
B
C
A (-2, 2)
y
x
A''= (-1, 2)
A''= (-1, -2)
A''= (2, -1)
A''= (-2, -1)
A'(       ,       )
∆ABC undergoes rx-axis then  T<-4, 3>
Find the coordinates of A' and A''
C
B
(5, 4)
A
A'(       ,       )
A''= (5, -4)
A''= (-9, 7)
A''= (1, -1)
A''= (1, 3)
∆ABC undergoes R180 then undergoes T<2, 2>
Find the coordinates of C' and C''
(-6, -1)
B
C
A
C'(         ,         )
C''= (8, -1) 
C''= (8, 3)
C''= (6, 1)
C''= (4, -1) 
∆ABC undergoes a composite transformation:   T(x,y) →(x-3,y-1) ○ R90 (ccw)Find the coordinates of A' and A''
B
C
(7, 2)
A
A' (       ,       )
A''= (-2, 7)
A''= (-1, 6)
A''= (-5, 6)
A''= (-1, -8)
∆ABC undergoes a composite transformation: ry-axis ○ R90 (ccw) 
Find the coordinates of A' and A''
B
C
A
A' (      ,      )
A''= (0, 3)
A''= (-3, 0)
A''= (3, 0)
A''= (0,-3)
∆ABC undergoes a composite transformation:  R180  R90 
Find the coordinates of A''
C
B
A
A''= (1, 1)
A''= (-1, 1)
A''= (0,0)
A''= (0,-1)
Which composite transformation maps ∆ABC onto ∆A''B''C''?
T<4, 3> ○ Rx-axis
T<4, 3> ○ Ry = -1
T<-4, -3>  ○ Ry = -1
Rx-axis  ○ T<4, 3>
∆ABC undergoes a composite transformation: T(x,y)→(x+3,y) ○ rx-axis
Find the coordinates of A''
B
C
A
(-3, 1)
A''= (1, 0)
A''= (0, 1)
A''= (-1,0)
A''= (0,-1)
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