Dilations
2/16/2017
A dilation is a transformation that:
•
Changes the size of a figure
•
Is not isometric
•
Enlarges or reduces by a scale factor
•
Has an image similar to its pre-image
𝐷0 , 2 𝑥 , 𝑦 = (2𝑥, 2𝑦)
𝐷𝑖𝑙𝑎𝑡𝑖𝑜𝑛𝑐𝑒𝑛𝑡𝑒𝑟 𝑜𝑓 𝑑𝑖𝑙𝑎𝑡𝑖𝑜𝑛 , 𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 𝑥 , 𝑦
= (𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 ∙ 𝑥 , 𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 ∙ 𝑦)
* This only works if the center of dilation is at
the origin.
The center of dilation is the
fixed point about which all
points grow or shrink
Example 1: Enlargement or Reduction?
Determine the scale factor
Example 2: Enlargement or Reduction?
Determine the scale factor
Example 3
Draw a dilation,
centered at the
origin, of
rectangle ABCD
by a scale factor
of 2 with vertices:
A(1, 1)
B(3, 1)
C(3, 2)
D(1, 2)
Example 4
1. Draw a dilation,
centered at the
origin, of triangle
J(-1, -1), K(-1, 2),
L(3, 1) by a scale
factor of 2.
2. Find the
perimeter of J’K’L’.
Example 5
1. Determine the
scale factor for the
dilation with center
O.
2. Write the notation
for this dilation.