october 18, 2017 - harlem122.org · 9.2 translations ink.notebook 1 october 18, 2017 page 122 9.2...

9.2 translations ink.notebook

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October 18, 2017

page 122

9.2 Translations

Visual TranslationVisual Translation

page 124page 123

Lesson Objectives Standards Lesson Notes

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9.2 Translations

Lesson Objectives


Lesson NotesStandards

After this lesson, you should be able to successfully translate a figure and describe the transformation.


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October 18, 2017

Lesson Objectives Standards


Lesson Notes

G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

A translation is a transformation which _________ each point of a figure the same ____________and in the same ______________.

Translations represent a _________ of a figure.

A translation maps each point to its image along a vector called the ______________ ___________.

x

yA TRANSLATION:

Every point in a figure moves the same distance in one or more directions within a plane


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October 18, 2017

To translate a point along vector

add a to the x-coordinate and add b to the y-coodinate.

(x, y) (x + a, y + b)

1. Rectangle RECT has vertices R(–2, –1), E(–2, 2), C(3, 2), and T(3, –1). Graph the figure and its image along the vector 〈2, –1〉. The vector indicates a translation ___ units to the ______ and ___ unit _____

x

y

(x, y) → (x + 2, y − 1)

R(–2, –1) → R′ ( _____ , _____ )

E(–2, 2) → E′ ( _____ , _____ )

C(3, 2) → C′ ( _____ , _____ )

T(3, –1) → T′ ( _____ , _____ )

Graph RECT and its image R′ E′ C′ T′.


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October 18, 2017

Graph each figure AND its image along the given vector. Graph VERY carefully. LABEL your Image Points accurately!!!

2) Quadrilateral TUVW with vertices T(–3, –8), U(–6,3),

V(0, 3) and W(3, 0); by vector 〈4, 5〉

Graph each figure AND its image along the given vector. Graph VERY carefully. LABEL your Image Points accurately!!!3. ËQRS with vertices Q(2, 5), R(7, 1),

and S(–1, 2); by vector 〈–3, –4〉

1. Draw a line through each vertex parallel to vector .

Draw the translation of the figure along the translation vector.

4. Start at the vertex and move in the same direction as the vector.

3. Locate the image of each point by marking off this distance along the line through each vertex.

2. Measure the length of vector . (tip to tail)

u

u


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October 18, 2017

becomes

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0

1

2

3

4

5

45°

Use the figure and the given translation vector. Then draw the translation of the figure along the translation vector.

nA

B

C

4.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0

1

2

3

4

5

90°

Use the figure and the given translation vector. Then draw the translation of the figure along the translation vector.

5.

A

BC

D

v

0

1

2

3

4

5

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

143°


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October 18, 2017

On the Worksheet

Practice

Use the figure and the given translation vector. Then draw the translation of the figure along the given translation vector.

1.


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October 18, 2017

Use the figure and the given translation vector. Then draw the translation of the figure along the given translation vector.

2.

3. ANIMATION Find the translation vector that moves the figure on the coordinate plane.

a) figure 1 → figure 2 〈___, ___〉

b) figure 2 → figure 3 〈___, ___〉

c) figure 3 → figure 4 〈___, ___〉

x

y

1

23

4

4. A TALE OF TWO TRANSLATIONS Lacy performs the translation (x, y) → (x + 5, y + 3) to an object in the coordinate plane. Kyle performs the translation (x, y) → (x − 4, y + 2) to the same object after Lacy. What single translation could have been done to achieve the same effect as Lacy and Kyle's combined translations? Would the result have been different if Kyle did his translation first?

''

''

Answers:

1.

3. a)〈4, 2〉b)〈–4, 1〉 c)〈3, 4〉


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October 18, 2017

Graph each figure AND its image along the given vector. Graph VERY carefully. LABEL your Image Points accurately!!!5. Quadrilateral LMNP with vertices L(4, 2), M(4, –1),

N(0, –1) and P(1, 4); by vector 〈–4, –3〉

Graph each figure AND its image along the given vector. Graph VERY carefully. LABEL your Image Points accurately!!!6. ËJKL with vertices J(–4, –4), K(–2, –1), and

L(2, –4); by vector 〈2, 5〉

Graph each figure AND its image along the given vector. Graph VERY carefully. LABEL your Image Points accurately!!! 7. Quadrilateral TUWX with vertices T(–1, 1), U(4, 2),

W(1, 5) and X(–1, 3); by vector 〈–2, –4〉

Graph each figure AND its image along the given vector. Graph VERY carefully. LABEL your Image Points accurately!!! 8. Pentagon DEFGH with vertices D(–1, –2),

E(2, –1), F(5, –2), G(4, –4) and H(1, –4); by vector 〈–1, 5〉


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October 18, 2017

10. SQUARES AND CIRCLESa) The image of square S under a translation is square S′.

Describe this translation. 〈___, ___〉

b) Draw the image of the circle C under the same translation that you described in Exercise A.

Answers:

P

L

MN

P'

L'

M'N'

5.

XT U

W

X'T' U'

W'

7.

9.b)9a)〈5, –1〉

october 18, 2017 - harlem122.org · 9.2 translations ink.notebook 1 october 18, 2017 page 122 9.2...

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