Dilations
A dilation is a chance in the ___________ of the figure. It does
not necessarily reflect a translation, rotation, or reflection.
This is Steve!
This is Steve after a
dilation of 50% or
after his size was
multiplied by 1/2.
Resulting image is
in actuality 1/4
times the size of
the original
Resulting image is
in actuality 4
times the size of
the original
This is Steve after a
dilation of 200% or
after his size was
multiple by 2.
A dilation changes everything in the image. Everything in the image changes in direct proportion to
everything else. If one side gets bigger, so does everything else. This is how a copy machine and
an overhead projector work.
A dilation is always represented using
the rule:
(x,y) = (Ax, Ay)
where A can be any number.
For each image below, write the coordinates for the image. Then, draw the image under the given magnitude.
Example 1.
ABC (x, y)
A'B'C' (2x, 2y)
A ( 1, 4 )
A’ (______, ______)
B (3, -1)
B’ (______, ______)
C (-2, -1)
C’ (______, ______)
This is a size change of magnitude _____.
This is an example of a(n) ______________-.
The area of the original triangle is ______.
The area of the new triangle is ______.
The new triangle is _____ as big.
Example 2.
DEF (x, y)
D'E'F' (1/2 x, 1/2y)
D (-8,-2)
D’ (______, ______)
E ( 2, -2)
E’ (______, ______)
F (-4, -6)
F’ (______, ______)
This is a size change of magnitude _______.
This is an example of a ______________-.
The area of the original triangle is ______.
The area of the new triangle is _______.
The new triangle is ______ as big.
Example 3.
Look at the coordinates below and give the magnitude of the dilation.
A.
X (3, -4) to X’ (9, -12)
magnitude: _____
B.
Y (-12, 15) to Y’ (-4, 5)
magnitude: _____
C.
Z (-1, 11) to Z’ (-5, 55)
magnitude: _____