ROTATIONS
The Earth
The Earth experiences one complete
rotation on its axis every 24 hours.
Windmills
Pinwheel
The blades on windmills convert the energy A children's toy that rotates when blown.
of wind into rotational energy.
Amusement Park Swing
Ferris Wheel
Merry-Go-Round
Amusement park rides, such as the swing,
allow you to become part of a rotation.
Ferris wheels rotate about a center hub.
(Yes, the seats tilt to prevent falling.)
On the merry-go-round, riders become
part of the rotation about the center of the
ride.
Rotations in the coordinate plane are counterclockwise.
Remember:
Clockwise:
Counterclockwise:
Rotation 90º:
Starting with ΔABC, draw the rotation of 90º
centered at the origin. (The rotation is
counterclockwise.)
To "see" that this is a rotation of 90º,
imagine point B attached to the red arrow.
The red arrow is then moved 90º (notice the
90º angle formed by the two red arrows).
Look at the new position of point B,
labeled B'. This same approach can be used
for all three vertices.
Rotation of 90º on coordinate axes.
Centered at origin.
(x, y) → (-y, x)
Rotation 180º:
Starting with ΔABC, draw the rotation of
180º centered at the origin. (The rotation
is counterclockwise.)
As we did in the previous example,
imagine point B attached to the red arrow
from the center (0,0). The arrow is then
moved 180º (which forms a straight line).
Notice the new position of B, labeled B'.
Rotation of 180º on coordinate axes.
Centered at origin.
(x, y) → (-x, -y)
(same as point reflection in origin)
Rotation 270º:
Starting with quadrilateral ABCD, draw
the rotation of 270º centered at the
origin. (The rotation is
counterclockwise.)
As we did in the previous examples,
imagine point A attached to the red arrow
from the center (0,0). The arrow is then
moved 270º (counterclockwise). Notice
the new position of A,
labeled A'. Since A was "on" the axis, A'
is also on the axis.
Rotation of 270º on coordinate axes.
Centered at orign.
(x, y) → (y, -x )