Geometry Notes SOL G.3 Transformations: Rotations, Dilations
Mrs. Grieser
Name: ___________________________________________ Date: ________________ Block: _______
Rotations

A rotation is a transformation that turns a figure about a
fixed point called the center of rotation

Rays drawn from the center of rotation to a point and its
image from the angle of rotation

Rotations are isometries (pre-image and image are congruent)

Positive angles rotate the figure in a counterclockwise direction; negative angles
rotate in a clockwise direction

A figure may be rotated any number of degrees around the center of rotation, but we
will concentrate on rules about these rotations around the origin:
o
90
o 180
o
270
Coordinate Rules for Rotations about the Origin
 90 rotation: x, y    y, x 
 180 rotation: x, y    x,  y 
 270 rotation: x, y    y,  x 
Example: Graph quadrilateral RSTU with vertices R(3, 1),
S(5, 1), T(5, -3), and U(2, -1). Then rotate the quadrilateral
270 about the origin.

R3, 1  R' ____________ 

S 5, 1  S ' ____________ 

T 5,  3  T ' ____________ 

U 2, - 1  U ' ____________ 
You try…
a) Rotate quadrilateral J(1, 4),
K(5, 5), L(7, 2), M(2, 2) 90
about the origin.
b) Given A(2, 3), B(2, -1),
C(-1, -1), graph the 90 ,
180 , and 270 rotations of
the ∆.
c) What are the number of
degrees separating the fan
blades?
Geometry Notes SOL G.3 Transformations: Rotations, Dilations
Mrs. Grieser Page 2
Dilations

A dilation is a transformation that produces an image that is the same shape as the
original, but is a different size (similar figure, so NOT an isometry)

Dilations are enlargements (“stretches”) or reductions (“shrinks”)

Scale factors are applied to the pre-image to create the image

We multiply points in the pre-image by the scale factor to create the image

Find scale factor by dividing a side length in the image by the corresponding side in the
pre-image

Scale factors bigger than 1 result in enlargements

Scale factors smaller than 1 but greater than 0 result in reductions
Coordinate Rules for Dilations:
If the center of dilation is the origin and the scale factor is k:
x, y   kx,
ky
Examples:
a) Draw the dilation image of ABC with b) Draw the dilation image of pentagon
the center of dilation at the origin
ABCDE with the center of dilation at
1
and a scale factor of 2 with points
the origin and a scale factor of
3
A(-2, -2), B(1, -1,), and C(0, 2).
with points
A(0, 0),
B(3, 3),
C(6, 3),
D(6, -2), and
E(3, -3).
You try…
a) A(2,3), B(2,-1), C(-1,-1)
Graph ABC and its image
using a dilation of 3.
b) Under a dilation, triangle
A(0, 0), B(0, 4), C(6, 0)
becomes triangle A'(0, 0),
B'(0, 10), C'(15, 0). What is
the scale factor for this
dilation?
c) What is the scale factor of
the dilation (with center at
the origin) shown?