LESSON
13.2
Algebraic Representations of
Dilations
How can you describe the effect of a dilation on coordinates
using an algebraic representation?
ADDITIONAL EXAMPLE 1
Graph the image of rectangle JKLM after a dilation
with the origin as its center and a scale factor of 2.
What are the vertices of the image?
The vertices of the dilated image are J' (2, 2), K'
(6, 2), L' (6, 8), and M' (2, 8).
13.2 LESSON QUIZ
8.3.C
1. A rectangle has vertices at P(6, 6), Q(6, –6),
R(–6, –6), and S(–6, 6). The origin is the center
of dilation, and
. What are the
vertices of the dilated image?
P'(2, 2), Q'(2, –2), R'(–2, –2), S'(–2, 2)
2. Write an algebraic representation of a dilation
that has a scale factor of 0.45.
(x, y)
(0.45x, 0.45y)
3. Triangle JKL is the preimage. Write two
algebraic representations, one for the dilation
to triangle J’K’L’ and one for the dilation to
triangle J’’K’’L’’.
Triangle J’K’L’: (x, y) (0.5x, 0.5y)
Triangle J’’K’’L’’: (x, y) (1.5x, 1.5y)
How can you describe the effect of a dilation on
coordinates using an algebraic representation?
Sample answer:
For scale factor k, the algebraic representation of
the dilation, with center at the origin, is
(x, y)
(kx, ky).