### Lesson #1

20
8β’3
-1
6
A Story of Ratios
15
Homework Helper
G8-M3-Lesson 1: What Lies Behind βSame Shapeβ?
1. Let there be a dilation from center ππ. Then, π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² , and π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² . Examine the
drawing below. What can you determine about the scale factor of the dilation?
I remember from the last
module that the original
points are labeled without
primes, and the images are
labeled with primes.
The dilation must have a scale factor larger than ππ, ππ > ππ,
since the dilated points are farther from the center than
the original points.
2. Let there be a dilation from center ππ with a scale factor ππ = 2. Then, π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² , and
π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(ππ) = ππβ² . |ππππ| = 1.7 cm, and |ππππ| = 3.4 cm, as shown. Use the drawing below to answer
parts (a) and (b). The drawing is not to scale.
I know that the bars around
the segment represent length.
So, |ππππβ² | is said, βThe length
of segment ππππ prime.β
a.
b.
Use the definition of dilation to determine |ππππβ² |.
definition of dilation in
class today. I should check
the Lesson Summary box to
review the definition.
|πΆπΆπΆπΆβ² | = ππ|πΆπΆπΆπΆ|; therefore, |πΆπΆπΆπΆβ² | = ππ β (ππ. ππ) = ππ. ππ and |πΆπΆπΆπΆβ² | = ππ. ππ ππππ.
Use the definition of dilation to determine |ππππβ² |.
|πΆπΆπΆπΆβ² | = ππ|πΆπΆπΆπΆ|; therefore, |πΆπΆπΆπΆβ² | = ππ β (ππ. ππ) = ππ. ππ and |πΆπΆπΆπΆβ² | = ππ. ππ ππππ.
Lesson 1:
G8-M3-HWH-1.3.0-09.2015
What Lies Behind βSame Shapeβ?
1
20
8β’3
-1
6
A Story of Ratios
15
Homework Helper
3. Let there be a dilation from center ππ with a scale factor ππ. Then, π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(π΅π΅) = π΅π΅β² , π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·π·(πΆπΆ) = πΆπΆ β² ,
and |ππππ| = 10.8 cm, |ππππ| = 5 cm, and |ππππβ² | = 2.7 cm, as shown. Use the drawing below to answer
parts (a)β(c).
a.
Using the definition of dilation with |ππππ| and |ππππβ² |, determine the scale factor of the dilation.
|πΆπΆπΆπΆβ² | = ππ|πΆπΆπΆπΆ|, which means ππ. ππ = ππ β (ππππ. ππ), then
ππ. ππ
= ππ
ππππ. ππ
ππ
= ππ
ππ
Use the definition of dilation to determine |ππππ |.
Since the scale factor, ππ,
ππ
ππ
is ,
ππ
then
|πΆπΆπΆπΆβ² |
ππ
= ππ |πΆπΆπΆπΆ|;
therefore, |πΆπΆπΆπΆβ² | = ππ β ππ = ππ. ππππ, and |πΆπΆπΆπΆβ² | =
ππ. ππππ ππππ.
Lesson 1:
G8-M3-HWH-1.3.0-09.2015
What Lies Behind βSame Shapeβ?
equality,
ππ
Since |ππ β²| = ππ|ππ |, then by
the multiplication property of
ππ
b.
β²
οΏ½πππ΅π΅β² οΏ½
|ππππ|
= ππ.
2