obj. 32 compositions of transformations

Obj. 32 Compositions

The student is able to (I can):

• Draw and identify compositions of transformations

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.

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

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.)

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

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)

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)