Obj. 32 Compositions of Transformations
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Obj. 32 Compositions
The student is able to (I can):
• Draw and identify compositions of transformations
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composition of transformations
Performing two or more transformations sequentially (one after another) to a figure.
An example that we have already seen of a composition is a glide reflection: we reflect the figure and then translate it along a vector.
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To describe a composite transformation using notation, state each of the transformations that make up the composite transformation and link them with the symbol �. The transformations are
performed in order from right to leftright to leftright to leftright to left.
Example: To perform the transformation
rx-axis — Reflect across the x-axis
R90°— Rotate 90° counterclockwise
T2, 4 — Translate along the vector ⟨2, 4⟩
° −� �2,4 90 x axisT R r
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With most compositions, it is important to perform them in the order given.
° −� x0 is9 axrR
− °�x axis 90Rr
(Reflect across the Reflect across the Reflect across the Reflect across the xxxx----axisaxisaxisaxis and then rotate 90rotate 90rotate 90rotate 90°°°°.)
(Rotate 90Rotate 90Rotate 90Rotate 90°°°° and then reflect across reflect across reflect across reflect across the xthe xthe xthe x----axisaxisaxisaxis.)
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Examples (a) Describe the composition
(b) Graph the transformations
1. (1, 4), (—2, 1), (—4, 1): T—3, 1 � ry-axis
2. (2, 1), (3, 5), (5, 2): R180°� ry=2
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Examples (a) Describe the composition
(b) Graph the transformations
1. (1, 4), (—2, 1), (—4, 1): T—3, 1 � ry-axis
a) Reflect across the y-axis and translate along the vector ⟨—3, 1⟩
b)
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Examples (a) Describe the composition
(b) Graph the transformations
2. (2, 1), (3, 5), (5, 2): R180°� ry=2
a) Reflect across the line y=2 and then rotate 180°.
b)