Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
Remember, in Math the word dilate means to __________________________________ or
________________________________________ a figure.
When you expand or shrink something, the __________________________________ tells
you by how much you need to expand or shrink it.
When scale factors are ____________________________ than 1, your figure gets bigger.
Examples: _________________________________________________________________
When scale factors are ____________________________ than 1, your figure gets smaller.
Examples: _________________________________________________________________
Example 1: Dilate a figure with a scale factor > 1 (Expand)
y-axis
Step 1: Identify
and record
each point’s
coordinates
J
K
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
-2
1
2
3
4
5
6
7
8
9
x-axis
L
-3
How Do I Dilate?
Step 2: Identify
the scale factor
and predict if it
will expand or
shrink.
-4
-5
-6
-7
-8
-9
Graph the dilated image of triangle JKL
using a scale factor of 2 and (0,0) as the
center of dilation.
J: __________
J’: __________
K: __________
K’: __________
L: __________
L’: __________
Step 3: Multiply
the coordinates
by the scale factor
and record the
new coordinates.
Step 4: Plot the
new points,
connect the dots,
and label the
image in prime
notation.
Step 5: Check your
work. Does your
image match your
prediction? Does it
make sense?
1
Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
You Try 1!
y-axis
y-axis
M
X
N
P
-9 -8 -7 -6 -5 -4
-3 -2
Y
-1 0
-1
1
2
-2
3
4
5
6
7
8
9
x-axis
-9 -8 -7 -6 -5 -4
-3 -2
1
2
3
4
5
6
7
8
9
x-axis
-2
O
-3
-1 0
-1
-3
-4
-4
-5
Z
-5
-6
-6
-7
-7
-8
-8
-9
-9
Graph the dilated image of quadrilateral
MNOP using a scale factor of 3 and the
origin as the center of dilation.
Graph the dilated image of triangle XYZ
using a scale factor of 1.5 and (0,0) as the
center of dilation.
M: __________
M’: __________
X: __________
X’: __________
N: __________
N’: __________
Y: __________
Y’: __________
O: __________
O’: __________
Z: __________
Z’: __________
P: __________
P’: __________
Example 2: Dilate a figure with a scale factor < 1 (Shrink)
y-axis
Graph the dilated image of triangle JKL
using a scale factor of 0.5 and (0,0) as the
center of dilation.
J
L
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
-2
1
2
3
4
5
6
7
8
9
J: __________
J’: __________
K: __________
K’: __________
L: __________
L’: __________
x-axis
-3
K
-4
-5
-6
-7
-8
-9
2
Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
You Try 2!
y-axis
y-axis
M
X
P
-9 -8 -7 -6 -5 -4
N
-3 -2
-1 0
-1
1
2
3
4
5
6
7
Y
8
9
-9 -8 -7 -6 -5 -4
x-axis
-3 -2
-1 0
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
-7
O
2
3
4
5
6
7
8
9
-7
Z
-8
1
-8
-9
-9
Graph the dilated image of quadrilateral
MNOP using a scale factor of 1/3 and
the origin as the center of dilation.
Graph the dilated image of triangle XYZ
using a scale factor of .5 and (0,0) as the
center of dilation.
M: __________
M’: __________
X: __________
X’: __________
N: __________
N’: __________
Y: __________
Y’: __________
O: __________
O’: __________
Z: __________
Z’: __________
P: __________
P’: __________
Example 3: Identify and describe a dilation.
y-axis
Given the coordinates for each set of vertices,
choose the appropriate transformation.
J’
L’
Triangle QRS
J
L
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
1
2
3
4
5
6
7
8
9
x-axis
Triangle Q’R’S’
Q: (6, 4)
Q’: (3, 2)
R: (0, 2)
R’: (0, 1)
S: (-8, -4)
S’: (-4, -2)
-2
K
K’
-3
-4
-5
-6
-7
-8
-9
A
B
C
D
Dilation with a scale factor of 2
Dilation with a scale factor of 0.5
Translation 1 unit down
Translation 3 units left
Describe the dilation of triangle JKL, using the origin
as the center.
________________________________________
3
x-axis
Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
You Try 3!
y-axis
P
Given the coordinates for each set of vertices,
choose the appropriate transformation.
M
P’
Triangle DEF
M’
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
-2
O’
1
2
3
4
5
6
7
8
9
x-axis
N’
Triangle D’E’F’
D: (6, 2)
D’: (3, 1)
E: (-1, 4)
E’: (-4, 3)
F: (-6, -3)
F’: (-9, -4)
-3
-4
N
-5
-6
-7
-8
O
-9
Describe the dilation of quadrilateral MNOP,
using the origin as the center.
A
B
C
D
Dilation with a scale factor of 0.5
Dilation with a scale factor of 2
Translation 3 units to the left, 1 unit down
Translation 3 units to the right, 1 unit down
________________________________________
Sample Test Question:
4
Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
Independent Practice
y-axis
1)
y-axis
2)
J’
A’
B’
A
B
J
L’
L
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
1
2
3
4
5
6
7
8
9
-9 -8 -7 -6 -5 -4
x-axis
-3 -2
-2
K
C
-4
-5
2
3
4
5
6
7
8
9
-3
-4
-6
C’
-7
-7
-8
-8
-9
K’
-9
Describe the dilation of quadrilateral ABCD,
using the origin as the center.
Describe the dilation of triangle JKL, using the
origin as the center.
________________________________________
________________________________________
y-axis
3)
x-axis
-5
-6
D’
1
-2
-3
D
-1 0
-1
y-axis
4)
N’
X’
X
N
M’
-9 -8 -7 -6 -5 -4
M
-3 -2
P
O’
O
-1 0
-1
1
2
3
4
5
7
8
9
x-axis
-9 -8 -7 -6 -5 -4
-2
Z
-7
-1 0
-1
3
4
5
6
7
8
9
x-axis
-5
Z’
-6
-7
-8
-9
-9
________________________________________
2
-3
-8
Describe the dilation of quadrilateral MNOP, using the
origin as the center.
1
-4
-5
-6
-3 -2
-2
-3
-4
P’
Y’
Y
6
Describe the dilation of triangle XYZ, using the
origin as the center.
________________________________________
5
Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
y-axis
5)
y-axis
6)
D
D’
A
A’
B
B’
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
1
2
3
4
5
6
7
8
9
x-axis
F’
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
-2
-2
-3
-3
C’
-4
-6
-7
-7
C
F
4
5
6
7
8
9
x-axis
-8
E
-9
3
-5
-6
-8
2
-4
E’
-5
1
-9
Describe the dilation of triangle ABC, using the
origin as the center.
Describe the dilation of triangle DEF, using the
origin as the center.
________________________________________
________________________________________
7) Given the coordinates for each set of vertices,
choose the appropriate transformation.
Triangle QRS
Triangle Q’R’S’
Q: (-2, 4)
Q’: (-4, 8)
R: (4, 0)
R’: (2, 4)
S: (6, 2)
S’: (4, 6)
y-axis
9)
A Dilation with a scale factor of 2
B Dilation with a scale factor of 0.5
C Translation 2 units left, 4 units up
D Translation 2 units right, 4 units up
-9 -8 -7 -6 -5 -4
-3 -2
-1 0
-1
1
2
3
4
5
6
7
8
9
x-axis
-2
-3
-4
-5
8) Given the coordinates for each set of vertices,
choose the appropriate transformation.
-6
-7
-8
Triangle ABC
Triangle A’B’C’
A: (9, 3)
A’: (3, 1)
B: (0, -6)
B’: (0, -2)
C: (-3, 0)
C’: (-1, 0)
A Dilation with a scale factor of 3
B Dilation with a scale factor of 1/3
-9
Create your own shape. Choose a scale factor
and dilate. Then, describe your dilation on the
lines below.
________________________________________
________________________________________
C Translation 2 units right
D Translation 4 units up
6
Name: __________________________________________
Unit 6: Transformational Geometry
Date: ___________________________
Lesson #4: SWBAT perform dilations on the coordinate plane
Homework: Homework #6.4
Exit Ticket
7