Geometry & Finite H
Mr. Russo
Name: _______________________
Date: _______________________
Dilations
A dilation is a transformation whose pre-image and image are similar, but not congruent. Therefore, a dilation
is not an ________________.
Dilations have a center (which is a __________ ) and a scale factor (which is a __________________ ).
The dilation is an enlargement if the scale factor is __________ than 1.
The dilation is a reduction if the scale factor is __________ than 1.
Given the center of the dilation, find the scale factor of the dilation, and circle if it is a reduction or an
enlargement.
Center = C
Center = C
Scale factor: ________
Scale factor: ________
Reduction
Enlargement
Reduction
Enlargement
Center = A
Center = O, OA’ = 5, OA = 15
Scale factor: ________
Scale factor: ________
Reduction
Enlargement
Reduction
Enlargement
Scale drawings and models are just dilations (usually reductions) of real life objects. Try these 2 problems.
The packaging lists a model car’s length as 7.6 cm. It also gives the scale as 1:63. What is the length of the
actual car in cm?
The height of a tractor-trailer truck is 4.2 m. The scale factor for a model of the truck is
1
. Find the height of
54
the model to the nearest tenth of a millimeter. (Watch your units.).
Suppose a dilation is centered at the origin. You can find the dilation image of a point by multiplying its
coordinates by the scale factor.
Scale factor of 4:  x, y    4 x, 4 y 
Given point P at (2, 1), plot…
image point A using a dilation with scale factor 3,
image point B using a dilation with scale factor 5, and
image point C using a dilation with scale factor ½,
all centered at the origin.
Label A, B, and C with their coordinates.
What do you notice about the images? ____________________________
One mo’ problem: ABC has vertices A(2,0), B(1, 12 ), C(1, 2) . What are the coordinates of the image of
ABC for a dilation with center (0, 0) and scale factor 4?
Now, take your calculator, go to the MATRIX menu (2nd-x-1), EDIT matrix A, make it 3  2, and put the
coordinates of vertices A, B, and C in the 3 rows. Then 2nd-MODE (to QUIT back to the home screen), and
type “4-2nd-MATRIX-1-ENTER.” What is the answer the same as?