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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 1 Rotations in the Coordinate Plane
Example 2 Angle of Rotation
Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.
1/2
Plot the 3 coordinates
Q(1, 1)
R(3, 4)
S(4, 1)
Label Q
Label R
Label SQ
R
S
Connect the dots in order that was plotted
Now the fun begins!
Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.
1/2
Q
R
S
1800 is half of a circle
1800 is a straight line
Let’s use the straight line definition of 1800
Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.
1/2
Q
R
S
Since the rotation is 1800 we will be plotting the image in the opposite quadrant as the original
Begin with Q(1,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0)
Label Q’
Q’
Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.
1/2
Q
R
S
Begin with R(3, 4) and draw a straight line into the opposite quadrant by passing through the origin (0, 0)
Label R’Q’
R’
Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.
1/2
Q
R
S
Begin with S(4,1) and draw a straight line into the opposite quadrant by passing through the origin (0, 0)
Label S’Q’
R’
S’
Connect the dots in order
Graph QRS with vertices Q(1, 1), R(3, 4), and S(4, 1). Then graph the image of QRS after a rotation of counterclockwise about the origin, and write the coordinates of its vertices.
1/2
Q
R
S
Q’
R’
S’
Q’(-1, -1)
R’(-3, -4)
S’(-4, -1)
Note: Since plotted in opposite quadrant then the numbers are the same just opposite signsAnswer:Must have the graph AND the coordinates
Answer: A'(–4, –1), B'(–2, –1), C'(–2, –4)
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.
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
2/2
Plot the 3 coordinates
X(2, 2)
Y(4, 3)
Z(3, 0)
Label X
Label Y
Label Z
XY
ZConnect the dots in order that was plotted
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
2/2
XY
Z
900 is one fourth a circle
900 makes a right triangle
Let’s use the right angle of 9000
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
2/2
XY
Z
Begin with X and draw a line to the origin
Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2)
From the origin make a right angle
Label X’
X’
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
2/2
XY
Z
Begin with Y and draw a line to the origin
Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2)
From the origin make a right angle
Label Y’
X’
Y’
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
2/2
XY
Z
Begin with Z and draw a line to the origin
Counterclockwise means to go to the left (From Quadrant 1 to Quadrant 2)
From the origin make a right angle
Label Z’
X’
Y’Z’
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
2/2
XY
Z
X’
Y’Z’
Connect the dots in order
X’(-2, 2)
Y’(-3, 4)
Z’(0, 3)
Answer:
Must have the graph AND the coordinates
1/2
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
A
BC
A’B’
C’
A’(-2, 1)
B’(-4, 1)
C’(-5, 5)
Answer:
Assignment
Lesson 6:9 Rotations 3 - 12 All
QUILTS Copy 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.
180° counterclockwise90° counterclockwise
Answer:
270° counterclockwise180° counterclockwise
QUILTS Copy 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:
