Composition of Transformations

[Pages:9]12 19 17 composition and sequence of rigid motions.notebook

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12/19 Aim: Composition of functions

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Do now:What is a composition?

Homework Worksheet

Test Wednesday and Thursday

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Composition SMARTDocumentCamera of Transformations

What is a composition of transformations?

A combination of two or more transformations in which the first transformation produces an image and the second transformation is performed on that image.

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Composition of Transformations The symbol we use to represent composition is a small open circle.

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Example: r xaxis T3, 4 is read as a reflection in the xaxis following a translation of (x +3, y + 4)

Example 1: What is the image of (2, 1) after r yaxis rx axis?

y

x

This composition is the same as______________

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Example 2: What is the image of (3, 4) after a r y = x T3, 4

y

Example 3: What is the image of point (2, 1) under r xaxis R180?

y

x

x

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Example 4: What is the image of (1, 5) under r y = 2 T2,1?

y

x

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Example 5: The coordinates of ABC are A(2, 1), B(5, 2) and C(4, 3). Graph and state the coordinates of A'B'C' after R90 r y axis?

y x

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A H

G F

B

C

p

D E

m

l

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A H

G F

B

C

p

D E

m

l

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The coordinates of GHK are G(3, 5), H(4, 3), and K(0, 0).

a) Graph GHK.

b) Graph G'H'K', the image of GHK under T2, 4.

c) Graph G"H"K", the image of G'H'K' under R180

d)

Graph

G"'H"'K"',

the

image

of

G"H"K"under y

r

x

=

2.

x

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homework last 2 pages

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stop

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12 1D9eta1c7hctohme plaosst iptiaogneand sequence of rigid motions.notebook do the do now:

How would you write symbolically this problem as a composition of transformations?

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When a sequence of rigid motions takes place with one rigid motion building off another, this is called a ______________________.

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1) To use the symbol as shown in this example: rx axis Ry axis(ABC)

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2) To use Function Notation as shown in this example: rk(Txy(AB) which means translate FIRST along vector XY and THEN reflect over line k. This is the notation we will be using.

A

A

A

Y

B

B

X

B

**** When performing or writing a composition, you must ALWAYS work from

_________________ to _______________!!

k

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Now let's watch a video where a sequence of rigid motions is performed.



1. What rigid motion(s) maps CD onto AB? Find to possible solutions. Write as a composition using function notation.

A

B

D

C

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12 19 17 composition and sequence of rigid motions.notebook

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The coordinates of GHK are G(3, 5), H(4, 3), and K(0, 0).

a) Graph GHK.

b) Graph G'H'K', the image of GHK under T2, 4.

c) Graph G"H"K", the image of G'H'K' under R180

d)

Graph

G"'H"'K"',

the

image

of

G"H"K"under y

r

x

=

2.

x

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