9.3—Rotations (isometric transformation)
A rotation is a transformation in which a figure is ______________ about a fixed point called the
_________________________.
The figure rotates through a specific _____________ in a specific ____________________.
Each point on the original is the _________________________ from the center as its corresponding
point on the image.
Rays drawn from the center of rotation to a point and its image form an angle called the
_________________________________________ (<QPQ’ below).
Rotations can be clockwise or counterclockwise.
Rotation Properties
A rotation about a point P through x is a transformation that maps every point Q in the plane to a
point Q’, so that the following properties are true:
Q’
Q
1. If Q is not point P, then QP = Q’P and mQPQ’ = x.
x
P
2. If Q’ is point P, then Q = Q’.
Assume all rotations are counterclockwise unless otherwise stated.
A rotation is an _______________ .
Rotations in a Coordinate Plane
In a coordinate plane, sketch the quadrilateral whose vertices are A(2, -2), B(4, 1), C(5, 1), and D(5, 1). Then, rotate ABCD 90 counterclockwise about the origin and name the coordinates of the new
vertices.
Figure ABCD
Figure A’B’C’D’
A(2, -2)
________
B(4, 1)
_________
C(5, 1)
________
D(5, -1)
________
Notice that the x-coordinate of the image is the
opposite of the y-coordinate of the preimage.
The y-coordinate of the image is the x-coordinate of the preimage.
90 Counterclockwise: (x, y) → _____
Here are the rules for common rotations about the origin:
90 Counterclockwise: (x, y) → _____
90 Clockwise: (x, y) → _______
180 Clockwise: (x, y) → ________
Example:
Name the coordinates of the vertices of the image
after a 90 clockwise rotation.
Name the coordinates of the vertices of the image
after a 90 counter clockwise rotation.
Name the coordinates of the vertices of the image
after a 180 counter clockwise rotation.