Clockwise and
8.10C
Counterclockwise Rotations
1. All rotations for this portion of the lesson are counterclockwise about the origin.

On the coordinate plane (page 2), draw a triangle in Quadrant I with the given coordinates. Label
the vertices A, B, and C. Record the coordinates of the vertices in the column below labeled 0°
rotation.

Using a sheet of patty paper, trace your x- and y– axes and copy triangle ABC. Make sure your
patty paper doesn’t move.

Place your pencil point on the origin of your coordinate plane and rotate your patty paper 90°
counterclockwise. Your patty paper is now in Quadrant __II___. Record the vertices of the
rotated triangle in the column below labeled 90°.

Now, rotate the patty paper 180° from the original position and record the coordinates of each of
the vertices of the rotated triangle. After a 180° rotation from the origin, you are now in
Quadrant _III_.

Rotate your patty paper 270° from the original position and record the coordinates of each of the
vertices of the rotated triangle. Your patty paper is now in Quadrant _IV_.

Finally, rotate your patty paper 360° from the original position and record the coordinates of each
of the vertices of the rotated triangle. Your patty paper is now in Quadrant _I_.
2. Draw the 4 rotated triangles on the coordinate plane to see how the triangles look when rotated.

How are your triangles alike?

What is the difference?
Their sides have the same length and they have the same angles.
They are rotated so their orientation is different.
Triangle
Vertices
0°
Rotation
90°
Rotation
180°
Rotation
270°
Rotation
360°
Rotation
A
(2, 0)
(0, 2)
(-2, 0)
(0, -2)
(2, 0)
B
(2, 4)
(-4, 2)
(-2, -4)
(4, -2)
(2, 4)
C
(7, 6)
(-6, 7)
(-7, 6)
(2, 0)
(2, 0)
(x,y)
(-y, x)
How the coordinates change
( -x
, -y
)
( y , -x
)
( x
,y
)
1
Coordinate Plane
Label and connect these vertices to form a triangle: A(2,0) B(2,4) C(7,6)
Quadrant
II
C
Quadrant
I
B
A
Quadrant
III
Quadrant
IV
2
2 Rotate 180°
1 Rotate 90°
3 Rotate 270°
Draw each rotation. Assume the rotations are counterclockwise about the origin.
1—Rotate 90°
2—Rotate 180°
Some coordinates in original figure.
Some coordinates in original figure.
( 0 , 4 ) ( 1,1 ) ( 2,0 )
(1
, 1
) (4
, 2
3—Rotate 270°
)(1
,3
Some coordinates in original figure.
(1
)
, -3
) (3
, -4
)(4
,0
)
Corresponding coordinates in image. Corresponding coordinates in image. Corresponding coordinates in image.
(-4
, 0
) (-1
, 1
)(0
, 2
) (-1
Describe the relationship in words.
,-1
(x,y)
(_-y_, __x__)
,-2
) (-1
,-3
) (
Describe the relationship in words.
Answers will vary
Describe the relationship with symbols.
) (-4
3 , 1
(x,y)
(_-x_, __-y__)
, 3
)(0
,4
)
Describe the relationship in words.
Answers will vary
Describe the relationship with symbols.
) (4
Answers will vary
Describe the relationship with symbols.
(x,y)
(_y_, __-x__)
3
4-Rotate 180°
5-Rotate 270°
6-Rotate 90°
Draw each rotation. Assume the rotations are clockwise about the origin.
4—Rotate 180°
5—Rotate 270°
Some coordinates in original figure.
(2
, 5
) (0
, 0
)(0
, 2
6—Rotate 90°
Some coordinates in original figure.
(-5
)
, 1
) (-3
, 0
) (-2,
4
Some coordinates in original figure.
) (-2
, -1)
(-4
, -3) (-1 ,-3)
Corresponding coordinates in image. Corresponding coordinates in image. Corresponding coordinates in image.
(-2
, -5) (0 , 0
)(0
, -2
) (-1
Describe the relationship in words.
,-5
(x,y)
(_-x_, __-y__)
,-3
) (-4
,-2
)
Describe the relationship in words.
Answers will vary
Describe the relationship with symbols.
) (0
( -1
(x,y)
(_-y, __x__)
) (-3,
4
) ( -3,
1
)
Describe the relationship in words.
Answers will vary
Describe the relationship with symbols.
, 2
Answers will vary
Describe the relationship with symbols.
(x,y)
(_y_, __-x__)
4