Download Scale factor

1. Have your homework out to be
stamped.
2. Complete the next 2 sections of
your SKILL BUILDER.
Name: __________________________________________ Date: ______________________ Period: ____
Weekly Homework 8th 2 - 6
Show all of your work to get credit.
MONDAY
1. The following pairs of angle measures are the measures of two angles of two triangles. Which pair of triangles
would be similar because they have two pair of congruent angles?
82˚
33˚
A 48° and 50°; 92° and 50°
18˚
92˚
B 102° and 60°; 28° and 60°
102˚
40˚
62˚
48˚
C 48° and 30°; 92° and 48°
D 48° and 70°; 62° and 70°
2. The side view of a roof is shown below.
x² + 21² = 25²
x² + 441 = 625
What is x, the height of the roof to the nearest tenth of a foot?
x² = 184
x = 13.56
x = 13.6
2-d
6h + 4
x -8
-10c² - 15
8k² - 24k + 12
x -21
x -12
Transformations:
Dilations
What is a Dilation?

Dilation is a transformation that produces a
figure similar to the original by proportionally
shrinking or stretching the figure.
Proportionally
Let’s take a look…
And, of course,
increasing the
circle
When a figure is dilated, it must be
proportionally
largera or
smaller
increases
the
So,
we always
have
circle
with a
diameter.
than thediameter.
original. We are just
certain
changing
the size or scale.
Decreasing
the
We have a circle
size of the
with a certain
circle
diameter.
decreases the
diameter.
 Same
shape, Different scale.
Which of these are dilations??
A
C
HINT: SAME SHAPE, DIFFERENT SIZE
D
B
Scale Factor and Center of
Dilation
When we describe dilations we use the terms scale factor
Scale factor
Here we have Igor. He is 3 feet
tall and the greatest width
across his body is 2 feet.
He wishes he were 6 feet tall
with a width of 4 feet.
He wishes he were larger by a
scale factor of 2.
Scale Factor


If the scale factor is larger than 1, the
figure is enlarged.
If the scale factor is between 1 and 0, the
figure is reduced in size.
Scale factor > 1
0 < Scale Factor < 1
Are the following enlarged or reduced??
C
A
Scale factor of 1.5
D
B
Scale factor of 0.75
Scale factor of 1/5
Scale factor of 3
The Object and the Image
B’



The original figure is
called the object and
the new figure is called
the image.
The object is labeled
with letters.
The image may be
labeled with the same
letters followed by the
prime symbol.
Image
C’
A’
B
Object
A
C
Let’s Try Some Dilations
Graph
ABC
10
Point A (3,4)
x2
A’(6,8)
8
Point B (3,2)
x2
B’(6,4)
6
Point c (5,2)
x2
C’(10,4)
4
Now let’s dilate by scale factor 2!!
A’
0
B’
A
2
2
C’
B
C
4
6
8
10
Name: ______________________________________________ Date: _____________
Dilation Activity
1. Imagine drawing a big “C” around the origin of your graph and use this
to help you label the quadrants I, II, III, and IV. The beginning of
the letter C is Quadrant I, and the others follow in order as you trace
the curve of the letter C.
2. Graph triangle ABC and dilate it with a scale factor of 3. Record the
coordinates of the dilated figure in the table below and graph the
dilation.
A
B
C
(-1,3)
(-1,-2)
(3,-2)
A’
B’
C’

In what quadrant does B’ lie?

How long is BC? How long is B’C’?

What is the scale factor for the length of a side on this
triangle?
1. Graph Quadrilateral WXYZ and dilate it with a scale factor of ½.
Record the coordinates of the dilated figure in the table below and
graph the dilation.
W
X
Y
Z
(-6,6)
(4,6)
(-8,-2)
(6,-2)
W’
X’
Y’
Z’

Is the dilated figure larger or smaller than the original? Why?

In what quadrant does the point X’ lie?
1. Graph Quadrilateral DOGS. Dilate the figure so that O’ has
coordinates of (4, 12). Record the coordinates of the dilated figure in
the table below and graph the dilation.
D
O
G
S
(-2,2)
(1,3)
(-2,-2)
(1,-1)
D’
O’
G’
S’

What scale factor was used to create quadrilateral D’O’G’S’?

Is the dilated figure larger or smaller than the original? Why?
2
If the figure below is dilated using a scale factor of ,
3
what will be the coordinates of A’?
A
2
( 2 , 2 )
3
2
If the figure below is dilated using a scale factor of,
1
what will be the coordinates of A’?
A
(2,2)