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Transparency 9. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 9-2b. Objective. Graph rotations on a coordinate plane. Example 9-2b. Vocabulary. Rotation. A transformation involving the turning or spinning of a figure around a fixed point.

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Transparency 9

Transparency 9

Click the mouse button or press the Space Bar to display the answers.


Splash screen

Splash Screen


Example 9 2b

Example 9-2b

Objective

Graph rotations on a coordinate plane


Example 9 2b1

Example 9-2b

Vocabulary

Rotation

A transformation involving the turning or spinning of a figure around a fixed point


Example 9 2b2

Example 9-2b

Vocabulary

Center of rotation

The fixed point a rotation of a figure turns or spins around


Example 9 2b3

Example 9-2b

Review Vocabulary

Angle of rotation

The degree measure of the angle through which a figure is rotated


Lesson 9 contents

Lesson 9 Contents

Example 1Rotations in the Coordinate Plane

Example 2Angle of Rotation


Example 9 1a

Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1a

Plot the 3 coordinates

R

Label Q

Q(1, 1)

Label R

R(3, 4)

Q

S

Label S

S(4, 1)

Connect the dots in order that was plotted

Now the fun begins!

1/2


Example 9 1a1

Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1a

1800 is half of a circle

R

Q

S

1800 is a straight line

Let’s use the straight line definition of 1800

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Example 9 1a2

Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1a

Since the rotation is 1800 we will be plotting the image in the opposite quadrant as the original

R

Q

S

Begin with Q(1,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0)

Q’

Label Q’

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Example 9 1a3

Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1a

Begin with R(3, 4) and draw a straight line into the opposite quadrant by passing through the origin (0, 0)

R

Q

S

Label R’

Q’

R’

1/2


Example 9 1a4

Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1a

Begin with S(4,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0)

R

Q

S

Label S’

S’

Q’

Connect the dots in order

R’

1/2


Example 9 1a5

Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRSafter a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1a

Q’(-1, -1)

R

R’(-3, -4)

S’(-4, -1)

Q

S

Note: Since plotted in opposite quadrant then the numbers are the same just opposite signs

S’

Q’

Answer:

Must have the graph AND the coordinates

R’

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Example 9 1b

Graph with vertices A(4, 1), B(2, 1), and C(2, 4). Then graph the image of after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.

Example 9-1b

Answer: A'(–4, –1), B'(–2, –1), C'(–2, –4)

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Example 9 2a

Example 9-2a

Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

Plot the 3 coordinates

Label X

X(2, 2)

Y

X

Label Y

Y(4, 3)

Label Z

Z(3, 0)

Z

Connect the dots in order that was plotted

2/2


Example 9 2a1

Example 9-2a

Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

900 is one fourth a circle

Y

900 makes a right triangle

X

Let’s use the right angle of 9000

Z

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Example 9 2a2

Example 9-2a

Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

Begin with X and draw a line to the origin

Y

X

X’

Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2)

Z

From the origin make a right angle

Label X’

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Example 9 2a3

Example 9-2a

Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

Begin with Y and draw a line to the origin

Y’

Y

X

X’

Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2)

Z

From the origin make a right angle

Label Y’

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Example 9 2a4

Example 9-2a

Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

Begin with Z and draw a line to the origin

Y’

Y

Z’

X

X’

Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2)

Z

From the origin make a right angle

Label Z’

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Example 9 2a5

Example 9-2a

Graph XYZ with vertices X(2, 2), Y(4, 3), and Z(3, 0) Then graph the image of XYZ after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

Connect the dots in order

Y’

X’(-2, 2)

Y

Z’

X

X’

Y’(-3, 4)

Z’(0, 3)

Z

Answer:

Must have the graph AND the coordinates

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Example 9 1b1

Example 9-1b

Graph ABC with vertices A(1, 2), B(1, 4), and C(5, 5) Then graph the image of ABC after a rotation 90° counterclockwise about the origin. Write coordinates of each vertices

C

C’

Answer:

B

A’(-2, 1)

B’(-4, 1)

A

B’

A’

C’(-5, 5)

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End of lesson 9

End of Lesson 9

Assignment


Example 9 2a6

Example 9-2a

QUILTSCopy and complete the quilt piece shown below so that the completed figure has rotational symmetry with 90°, 180°, and 270°,as its angles of rotation.

1st copy the pattern


Example 9 2a7

Example 9-2a

Rotate the figure 90, 180, and 270 counterclockwise. Use a 90 rotation clockwise to produce the same rotation as a 270 rotation counterclockwise.

90° counterclockwise


Example 9 2a8

Example 9-2a

Rotate the figure 90, 180, and 270 counterclockwise. Use a 90 rotation clockwise to produce the same rotation as a 270 rotation counterclockwise.

90° counterclockwise

180° counterclockwise


Example 9 2a9

270° counterclockwise

Example 9-2a

Answer:

180° counterclockwise


Example 9 2b4

Example 9-2b

*

QUILTSCopy and complete the quilt piece shown below so that the completed figure has rotational symmetry with 90°, 180°, and 270°,as its angles of rotation.


Example 9 2b5

Example 9-2b

Answer:


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