Check 12-2 HW

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12-3 Graphing Translation

6th Grade Math HOMEWORK

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12-1 Tables and Functions

Our Learning GoalStudents will

understand functions by creating tables and graphing translations.

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12-1 Tables and Functions

Students will understand functions by creating tables and graphing translations.

• Learn to use data in a table to write an equation for a function and to use the equation to find a missing value.

• Learn to represent linear functions using ordered pairs and graphs.

• Learn to use translations to change the positions of figures on a coordinate plane.

• Learn to use reflections to change the positions of figures on a coordinate plane.

• Learn to use rotations to change positions of figures on a coordinate plane.

• Learn to visualize and show the results of stretching or shrinking a figure.

Today’s Learning Goal Assignment

Learn to use translations to change the positions of figures on a coordinate plane.

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12-3 Graphing Translation

12-3 Graphing Translations

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm Up

1. Use the given x-values to write solutions of the following equation as ordered pairs. y = 6x – 2 for x = 0, 1, 2, 3

2. Determine whether (3, –13) is a solution to the equation y = –4x – 1.

(0, –2), (1, 4), (2, 10), (3, 16)

yes

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12-3 Graphing Translation

Problem of the Day

Samantha’s house is 3 blocks east and 5 blocks south of Tyra. If Tyra walks straight south and then straight east to Samantha’s house, does she walk more blocks east or more blocks south? How many more?

south; 2 blocks

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12-3 Graphing Translation

A translation is a movement of a figure along a straight line. You can translate a figure on a coordinate plane by sliding it horizontally, vertically, or diagonally.

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12-3 Graphing Translation

Additional Example 1: Translating Figures on a Coordinate Plane

Give the coordinates of the vertices of the figure after the given translation.

Translate triangle DEF 4 units left and 3 units up.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

654321

-1-2-3-4-5-6

F

D

E

y

x

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12-3 Graphing Translation

Additional Example 1 Continued

To move the triangle 4 units left, subtract 4 from each of the x-coordinates.

To move the triangle 3 units up, add 3 to each of the y-coordinates.

DEF D’E’F’

D(1, 4)

E(4, 2)

F(–3, –3)

D’(1 – 4, 4 + 3) D’(–3, 7)

E’(0, 5)

F’(–7, 0)

E’(4 – 4, 2 + 3)

F’(-3 – 4, –3 + 3)

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12-3 Graphing Translation

Additional Example 1 Continued

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

543

1

-2-3

-5-6

6

2

-1

-4

E’

F’

D’ y

x

F

D

E

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12-3 Graphing Translation

Try This: Example 1

Give the coordinates of the vertices of the figure after the given translation.

Translate triangle GHJ 3 units left and 3 units up.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

654321

-1-2-3-4-5-6

J

G H

y

x

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12-3 Graphing Translation

Try This: Example 1

To move the triangle 3 units left, subtract 3 from each of the x-coordinates.

To move the triangle 3 units up, add 3 to each of the y-coordinates.

GHJ G’H’J’

G(2, 4)

H(4, 4)

J(–3, –2)

G’(2 – 3, 4 + 3) G’(–1, 7)

H’(1, 7)

J’(–6, 1)

H’(4 – 3, 4 + 3)

J’(–3 – 3, –2 + 3)

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12-3 Graphing Translation

Try This: Example 1 Continued

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

543

1

-2-3

-5-6

6

2

-1

-4

H’

J’

G’ y

x

J

G H

x

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12-3 Graphing Translation

Additional Example 2: Music Application

Members of a marching band begin in a trapezoid formation represented by trapezoid KLMN. Then they move 4 steps right and 5 steps down. Give the coordinates of the vertices of the trapezoid after such a translation.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

654321

-1-2-3-4-5-6

M

K L

y

x

N

-7-8

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12-3 Graphing Translation

Additional Example 2 Continued

To move 4 steps right, add 4 to each of the x-coordinates.

To move 5 steps down, subtract 5 from each of the y-coordinates.

KLMN K’L’M’N’

K(–2, 1)

L(1, 1)

M(3, –3)

K’(–2 + 4, 1 – 5) K’(2, –4)

L’(5, –4)

M’(7, –8)

L’(1 + 4, 1 – 5)

M’(3 + 4, –3 – 5)

N(–4, –3) N’(0, –8)M’(–4 + 4, –3 – 5)

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12-3 Graphing Translation

Additional Example 2 Continued

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

654321

-1-2-3-4-5-6

M

K L

y

x

N

-7 M’

K’ L’

N’-8

x

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12-3 Graphing Translation

Try This: Example 2

Members of a flag team begin in a trapezoid formation represented by trapezoid KLMN. Then they move 3 steps right and 2 steps down. Give the coordinates of the vertices of the trapezoid after such a translation.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

654321

-1-2-3-4-5-6

M

K L

y

x

N

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12-3 Graphing Translation

Try This: Example 2

To move 3 steps right, add 3 to each of the x-coordinates.

To move 2 steps down, subtract 2 from each of the y-coordinates.

KLMN K’L’M’N’

K(–1, 3)

L(1, 3)

M(3, –1)

K’(–1 + 3, 3 – 2) K’(2, 1)

L’(4, 1)

M’(6, –3)

L’(1 + 3, 3 – 2)

M’(3 + 3, –1 – 2)

N(–3, –1) N’(0, –3)M’(-3 + 3, –1 – 2)

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12-3 Graphing Translation

Try This: Example 2 Continued

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

654321

-1-2-3-4-5-6

M

K L

y

N

x

M’

K’ L’

N’

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12-3 Graphing Translation

Lesson Quiz

Give the coordinates of the vertices of triangle ABC, with vertices A(-5, -4), B(-3, 2), and C(1, -3), after the given translations.

1. Translate triangle ABC 3 units up and 2 units

right.

2. Translate triangle ABC 5 units down and 3 units

left.

3. Translate triangle ABC 2 units down and 4 units

right.

A’(-3, -1), B’(-1, 5), and C’(3,0)

Insert Lesson Title Here

A’(-8, -9), B’(-6, -3), and C’(-2,-8)

A’(-1, -6), B’(1, 0), and C’(5,-5)

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12-3 Graphing Translation