Download Holt Geometry 12-7

12-7 Dilations
Objective
Identify and draw dilations.
Holt Geometry
12-7 Dilations
Recall that a dilation is a transformation that
changes the size of a figure but not the shape.
The image and the preimage of a figure under a
dilation are similar.
Holt Geometry
12-7 Dilations
Example 1: Identifying Dilations
Tell whether each transformation appears to
be a dilation. Explain.
A.
No; the figures are not
similar.
Holt Geometry
B.
Yes; the figures are
similar and the image is
not turned or flipped.
12-7 Dilations
Example 1a
Tell whether each transformation appears to
be a dilation. Explain.
a.
b.
No, the figures are
not similar.
Holt Geometry
Yes, the figures are
similar and the image
is not turned or
flipped.
12-7 Dilations
A dilation enlarges or reduces all dimensions
proportionally. A dilation with a scale factor
greater than 1 is an enlargement, or expansion.
A dilation with a scale factor greater than 0 but
less than 1 is a reduction, or contraction.
Holt Geometry
12-7 Dilations
Holt Geometry
12-7 Dilations
If the scale factor of a
dilation is negative, the
preimage is rotated by
180°. For k > 0, a dilation
with a scale factor of –k is
equivalent to the
composition of a dilation
with a scale factor of k that
is rotated 180° about the
center of dilation.
Holt Geometry
12-7 Dilations
Example 2: Drawing Dilations in the Coordinate Plane
Draw the image of the triangle with vertices
P(–4, 4), Q(–2, –2), and R(4, 0) under a
dilation with a scale factor of
origin.
The dilation of (x, y) is
Holt Geometry
centered at the
12-7 Dilations
Example 2 Continued
Graph the preimage and image.
P
R’
Q
Holt Geometry
Q’
R
P’