Transformation Packet - Winston-Salem/Forsyth County Schools

[Pages:43]Name: ________________________________

Date: __________________

M8-U3: Notes #1 ? Transformational Geometry -Translations Class: __________________

A transformation is a change in the __________, _______________, or ______________ of a figure.

A translation is a transformation which ____________ each point of a figure the same ____________ and in the same ________________.

The resulting figure after a transformation is called the ___________ of the original figure.

EXAMPLE 1: ABC is translated 1 unit right and 4 units up. Draw the image A'B'C'.

What are the coordinates of:

A (1, -3)

A' _________

B (3, 0)

B' _________

C (4, -2)

C'__________

From EXAMPLE 1, ABC A'B'C' As a general rule this translation could be written as (x, y) (x + ___, y + ___ ).

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EXAMPLE 2:

JKL has coordinates J (0,2), K (3,4), and L (5,1).

a) Draw JKL. b) Draw the image J'K'L' after a translation of 4 units to the left and 5 units up. Label the triangle.

What are the coordinates of:

J

(0, 2) J' _________

K (3, 4) K' _________

L (5, 1) L'__________

Rule: (x, y) (

,

)

y 10

9 8 7 6 5 4 3 2 1

?10 ?9 ?8 ?7 ?6 ?5 ?4 ?3 ?2 ?1 ?1 ?2 ?3 ?4 ?5 ?6 ?7 ?8 ?9

?10

1 2 3 4 5 6 7 8 9 10 x

Tell me more about this figure, is it congruent or similar? Explain how you know.

x coordinate y coordinate

Translation Location Add

Subtract

2

EXAMPLE 3: Write a general rule which describes the translation shown below. LMN is the original triangle.

(x, y) (

,

)

EXAMPLE 4:

a) Graph points T(0,3), U(2, 4) and V(5, -1) and connect the points to make a triangle.

b) Translate TUV using the rule (x, y) (x - 3, y - 1).

y

c) In words, describe what the rule is asking you to do.

5

4

3

2

1

d) Draw the image T'U'V'. e) Identify the coordinates of T'U'V'.

T' U' V'

?5 ?4 ?3 ?2 ?1 ?1 ?2 ?3 ?4 ?5

12345 x

f) Using the image of T'U'V' perform an additional translation using the rule (x, y) (x + 3, y - 3). State the new coordinates of T"U"V". Is this new image congruent or similar to

the original figure?

3

Practice: 1) a) Use arrow notation to write a rule for the given translation.

_______________________________

b) Graph and label the image after the translation. c) Name the coordinates of the image.

A' _____________ B' _____________ C' _____________ D' ____________

2) a) Use arrow notation to write a rule for the given translation.

___________________________________

b) Graph and label the image after the translation.

c) Name the coordinates of the image.

A' _____________

B' _____________

C' _____________

D' _____________

In questions 3 and 4 below, use arrow notation to write a rule that describes the translation shown on the graph.

3)

4)

4

5) MULTIPLE CHOICE:

Write a description of the rule x, y x 7, y 4.

(a) translation 7 units to the right and 4 units up (b) translation 7 units to the left and 4 units down (c) translation 7 units to the right and 4 units down (d) translation 7 units to the left and 4 units up

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Name: _________________________________ M8-U3: HW #1 ? Translations

Date: _______________________ Class: ______________________

1. Draw the translation of the triangle HOT six units left and one unit down. Label the image H'O'T'. Is the image similar or congruent? How do you know?

y 7

6

5

O

4

3

2

1

H

?7 ?6 ?5 ?4 ?3 ?2 ?1 ?1

T

1 2 3 4 5 6 7x

?2

?3

?4

?5

?6

?7

2. Find the translation of the quadrilateral WXYZ under the rule

(x, y) x 2, y 4.

y 8

7

6

5

4

3

X

2

1

W

?8 ?7 ?6 ?5 ?4 ?3 ?2 ?1 ?1

?2

1 2 3 4 5 6 7 8x

Y

?3

?Z4

?5

?6

?7

?8

6

Use the grid below to answer questions 3 through 5.

y

E8 A

6

4

C

2

?8 ?6 ?4 ?2 ?2

?4

?6

B

?8

2 4 6 8x

D

3. Find the rule to describe the translation from point A to point B.

4. Find the rule to describe the translation from point C to point D.

5. Find the rule to describe the translation from point E to point A.

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6. Quadrilateral ABCD is plotted on the grid below. Part A On the graph, draw the translation of polygon ABCD eight units to the left and seven units down. Label the image A'B'C'D'.

Part B On the lines below, explain how you determined the location of A'. ________________________________________________________ ________________________________________________________ ________________________________________________________

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