DILATIONS & ROTATIONS
SECONDARY 1 MATH
Dilation
a transformation in which a polygon is enlarged or reduced by a given factor
around a given center point
multiply the dimensions of the pre-image by the factor to get the dimensions
of the image
Scale Factor
image dimensions
pre-image dimensions
the amount by which an image is enlarged or reduced
k
0 < k < 1 🡪
reduction
k = 1 🡪
no dilation
k > 1 🡪
enlargement
shape gets
smaller
shape stays same size
shape gets
LARGER
Dilation Notation
(if the origin is used as center of dilation)
I’ M’
T’ E’
area of T’I’M’E’ is 9
times the area of TIME
each dimension (length & width)
changed by a scale factor of 3
Multiply each by 3
2 square units
18 square units
enlargement
k = 4
W’ A’
S’ B’
S’ ( 0 , 4 )
W’ ( 4 , 12 )
A’ ( 12 , 12 )
B’ ( 16 , 4 )
reduction
E’ ( 5 , 4 )
P’ ( 5 , 3 )
I’ ( 2 , 3 )
C’ ( 2 , 4 )
C’ E’
I’ P’
A figure is shown along with it’s image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find scale factor
distance to the image
distance to the pre-image
6
14
Reduction
A figure is shown along with it’s image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find scale factor
distance to the image
distance to the pre-image
10
7
Enlargement
leave as improper fraction
A figure is shown along with it’s image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find scale factor
distance to the image
distance to the pre-image
10
18
Reduction
Rotation
a transformation that turns a shape around a point in a circular motion
distance of each point on the shape to the center of rotation must stay the
same after the rotation occurs
same specific angles are formed between points on the pre-image and image
SPIN
TURN
Directions
Clockwise
Counterclockwise
A’
A
moves from Quadrant II to Quadrant I
90º means perpendicular,
so slopes must be negative reciprocals
A’ ( 7 , 5 )
NOT (5,7)
reflection ☹
C
B
Slope from origin to
B
B’
C
C’
B’ ( 1 , 6 )
C’ ( −3 , 4 )
B’
C’
F
E
D
D’
E’
F’
D’ (−5 , 2 )
E’ ( −1 , 5 )
F’ ( 1 , 3 )
Notice the relationship between pre-image
coordinates and image coordinates
coordinates switched places and
new y-coordinate changed its sign
Q
P
R
S
P’ (−2 , 3 )
Q’ ( −3 , 8 )
R’ ( 2 , 9 )
S’ ( 4 , 5 )
coordinates switched places and
new x-coordinate changed its sign
P’
Q’
R’
S’
Q
P
M
M’ ( 2 , 4 )
P’ ( 4 , 1 )
Q’ ( 1 , −1 )
both coordinates changed their signs
M’
P’
Q’
Rotation Notation
Pre-image