Warm-Up
Exercises
Bell Work
If
ABC ~ DEF, find each value.
1.
EF
2. AC
3. scale factor
Warm-Up
Exercises
Notes
Warm-Up1Exercises
EXAMPLE
Find the scale factor of the dilation. Then tell whether
the dilation is a reduction or an enlargement.
a.
Warm-Up1Exercises
EXAMPLE
Find the scale factor of the dilation. Then tell whether
the dilation is a reduction or an enlargement.
b.
Warm-Up2Exercises
EXAMPLE
Draw and label DEFG. Then construct a dilation
of DEFG with point D as the center of dilation and
a scale factor of 2.
SOLUTION
STEP 1
Draw DEFG. Draw rays from D through vertices E, F,
and G.
Warm-Up2Exercises
EXAMPLE
Draw a dilation
STEP 2
Open the compass to the length of DE . Locate
E’ on DE so DE’ = 2(DE). Locate F’ and G’ the
same way.
Warm-Up2Exercises
EXAMPLE
Draw a dilation
STEP 3
Add a second label D’ to point D. Draw the
sides of D’E’F’G’.
Warm-Up
Exercises
GUIDED
PRACTICE
1. In a dilation, CP’ = 3 and CP = 12. Tell whether the
dilation is a reduction or an enlargement and find its
scale factor.
Warm-Up
Exercises
GUIDED
PRACTICE
2. Draw and label RST. Then construct a dilation
of RST with R as the center of dilation and a
scale factor of 3.
ANSWER
Warm-Up
Exercises
Notes
Definitions
Scalar multiplication is the process of multiplying each
element of a matrix by a real number or scalar.
Warm-Up
Exercises
GUIDED
PRACTICE
Simplify the product.
2 1 –10
3.
5
3 –4
7
[
]
Warm-Up
Exercises
GUIDED
PRACTICE
Simplify the product.
4.
[
–2
–4 1 0
9 – 5 –7
]
Warm-Up4Exercises
EXAMPLE
The vertices of quadrilateral KLMN are K(– 6, 6), L(– 3, 6),
M(0, 3), and N(– 6, 0). Use scalar multiplication to find
the image of KLMN after a dilation with its center at the
origin and a scale factor of 1 . Graph KLMN and its
3
image.
SOLUTION
K L M N
[
K’ L’ M’ N’
][
]
1 –6–3 0 –6
–2–1 0 –2
=
3
2 2 1 0
6 6 3 0
Scale
factor
Polygon
matrix
Image
matrix
Warm-Up
Exercises
GUIDED
PRACTICE
5. The vertices of RST are R(1, 2), S(2, 1), and T(2, 2). Use
scalar multiplication to find the vertices of R’S’T’
after a dilation with its center at the origin and a scale
factor of 2.
Warm-Up5Exercises
EXAMPLE
The vertices of ABC are A(– 4, 1), B(– 2, 2), and C( – 2, 1).
Find the image of ABC after the given composition.
Translation: (x, y)
(x + 5, y + 1)
Dilation: centered at the origin with a scale factor of 2
Warm-Up
Exercises
GUIDED
PRACTICE
6. A segment has the endpoints C( –1, 1) and D(1, 1).
Find the image of CD after a 90° rotation about the
origin followed by a dilation with its center at the
origin and a scale factor of 2.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
1.
Find the scale factor. Tell whether the dilation is
reduction or an enlargement. Find the value of x.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
2.
Find the image matrix that represents a dilation of
XYZ with vertices X(3,2), Y(8,–1) and Z(–1,–1)
centered at the origin with scale factor 1 .
2
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
3.
𝟏
𝟔
𝟓 𝟑
−𝟐 𝟐
−𝟒
𝟏
Warm-Up
Exercises
For Tomorrow
Homework
HW: 9.7 (pg. ) #