course 1 12-5 graphing rotations check 12-4 hw none!

Course 1

12-5 Graphing Rotations

Check 12-4 HW

None!

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6th Grade Math HOMEWORK

Page 630#17-18

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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 rotations to change positions of figures on a coordinate plane.

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpParallelogram ABCD has vertices (-4, 1), (0, 1), (–3, 4), and (1, 4).

1. What are the vertices of ABCD after it has been reflected across the x-axis?

2. What are the vertices after is has been reflected across the y-axis?

(–4, –1), (0, –1), (–3, –4), (1, –4)

(4, 1), (0, 1), (3, 4), (–1, 4)

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Problem of the Day

If each of the capital letters of the alphabet is rotated a half turn around its center, which will look the same?

H, I, N, O, S, X, Z

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You can rotate a figure about the origin or another point on a coordinate plane.

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A rotation is the movement of a figure about a point. Rotating a figure “about the origin” means that the origin is the center of rotation.

Remember!

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-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

Additional Example 1: Rotating Figures on a Coordinate Plane

E F

GH

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Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH clockwise 90° about the origin.

Additional Example 1 Continued

The new x-coordinates are the old y-coordinates.

The new y-coordinates are the opposites of the old x-coordinates.

EFGH E’F’G’H’

E(–4, 0) E’(0, 4)

F(0, 0) F’(0, 0)

G(–2, –3) G’(–3, 2)

H(–6, –3) H’(–3, 6)

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Additional Example 1 Continued

Rotate parallelogram EFGH 90° about the origin.

-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

xE F

GH

F’

E’

G’

H’

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-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

Try This: Example 1

Give the coordinates of the vertices of the figure after the given rotation. Rotate parallelogram EFGH counterclockwise 180° about the origin.

E F

GH

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Try This: Example 1 Continued

The new x-coordinates are the opposites of the old x-coordinates.

The new y-coordinates are the opposites of the old y-coordinates.

EFGH E’F’G’H’

E(–4, 0) E’(4, 0)

F(0, 0) F’(0, 0)

G(–2, –3) G’(2, 3)

H(–6, –3) H’(6, 3)

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-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

Try This: Example 1 Continued

Rotate parallelogram EFGH counterclockwise 180° about the origin.

E F

GH

E’F’

G’ H’

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Additional Example 2A: Art Application

An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin.

-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

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ABCDE A’B’C’D’E’

A(0, 0) A’(0, 0)

B(1, 4) B’(4, –1)

C(3, 5) C’(5, –3)

D(7, 3) D’(3, –7)

Additional Example 2A Continued

E(6, 0) E’(0, –6)



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Additional Example 2A Continued

Rotate the figure after a clockwise 90° about the origin.

-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

C’

D’

B’A’

E’

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A(–6, 0) A’(0, 6)

B(–5, 4) B’(4, 5)

C(–3, 5) C’(5, 3)

D(1, 3) D’(3, –1)

Try This: Example 2A Continued

E(0, 0) E’(0, 0)



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Try This: Example 2A

An artist draws this figure. She rotates the figure without changing its size or shape. Give the coordinates of the vertices of the figure after a clockwise rotation of 90° about the origin.

-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

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Try This: Example 2A Continued


-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

C’

D’

B’A’

E’

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B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin.

Additional Example 2B: Art Application

-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

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Additional Example 2B Continued


A(0, 0) A’(0, 0)

B(1, 4) B’(–1, –4)

C(3, 5) C’(–3, –5)

D(7, 3) D’(–7, –3)

E(6, 0) E’(–6, 0)

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Additional Example 2B Continued


-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

C’

D’ B’

A’E’

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B. Give the coordinates of the vertices of the figure after a counterclockwise rotation of 180° about the origin.

Try This: Example 2B

-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

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Try This: Example 2B Continued


A(–6, 0) A’(6, 0)

B(–5, 4) B’(5, –4)

C(–3, 5) C’(3, –5)

D(1, 3) D’(1, –3)

E(0, 0) E’(0, 0)

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Try This: Example 2B Continued


-8 -6 -4 -2 2 4 6 8

8

2

4

6

-2

-4

-6

-8

y

x

C

DB

A E

C’D’ B’

A’E’

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Lesson Quiz

Give the coordinates of the vertices of the trapezoid after the given rotation.

1. Rotate trapezoid ABCD counterclockwise 180° about the origin.

2. Rotate trapezoid ABCD clockwise 90° about the origin.

A’(0, 5), B’(0, 0), C’(–3, 1), D’(–3, 4)

A’(5, 0), B’(0, 0), C’(1, 3), D’(4, 3)

Insert Lesson Title Here

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course 1 12-5 graphing rotations check 12-4 hw none!

Documents

efgh additional example

clockwise rotation

positions of figures

vertices of abcd

coordinate planeefghgive

rotating figures

given rotation

b continuedabcdeabcdea0