Identify and draw rotations

1. Rotations
The student is able to (I can):
• Identify and draw rotations

2. rotationrotationrotationrotation – a transformation that turns a figure around a fixed
point, called the center of rotation.

center of
rotation

3. In the coordinate plane, we will look at three specific types of
rotations (CCW = counter clockwise; CW = clockwise):
90° CCW about the origin
90° CW about the origin
180° about the origin
yP´(–y, x)

( , ) ( , )x y y x 
( , ) ( , )x y x y  
( , ) ( , )x y y x 
x

P(x, y)

90909090°°°°

P´(–x, –y)
180180180180°°°°
P´(y, –x)
90909090°°°°

4. Examples
1. Rotate ΔRUG with vertices R(2, –1), U(4, 1), and G(3, 3)
by 90° CCW about the origin.
90° CCW:
2. Rotate ΔTRI with vertices T(2, 2), R(4, –5), and I(–1, 6) by
180° about the origin.
( , ) ( , )x y y x 
180° about the origin.
180°: ( , ) ( , )x y x y  

5. Examples
1. Rotate ΔRUG with vertices R(2, –1), U(4, 1), and G(3, 3)
by 90° CCW about the origin.
90° CCW:
RRRR´´´´(1, 2),(1, 2),(1, 2),(1, 2), UUUU´´´´((((––––1111, 4),, 4),, 4),, 4), GGGG´´´´((((----3, 3)3, 3)3, 3)3, 3)
2. Rotate ΔTRI with vertices T(2, 2), R(4, –5), and I(–1, 6) by
180° about the origin.
( , ) ( , )x y y x 
180° about the origin.
180°:
TTTT´´´´((((––––2222,,,, ––––2222),),),), RRRR´´´´((((––––4444, 5),, 5),, 5),, 5), IIII´´´´(1,(1,(1,(1, ––––6666))))
( , ) ( , )x y x y  