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Objective

Graph rotations on a coordinate plane

Vocabulary

Rotation

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

Vocabulary

Center of rotation

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

Review Vocabulary

Angle of rotation

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

Example 1Rotations in the Coordinate Plane

Example 2Angle of Rotation

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.

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

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.

1800 is half of a circle

R

Q

S

1800 is a straight line

Let’s use the straight line definition of 1800

1/2

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.

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’

1/2

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

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

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’

1/2

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.

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

1/2

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

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

2/2

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’

2/2

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’

2/2

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’

2/2

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

2/2

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)

1/2

Assignment

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

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

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

270° counterclockwise

Answer:

180° counterclockwise

*

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.

Answer: