Investigation 2.1
Drawing Wumps
Stretching & Shrinking
Zach and Marta’s computer game
involves a family called the Wumps.
The members of the Wump family
are various sizes, but they all have
the same shape. That is, they are
similar. Mug Wump is the game’s
main character. By enlarging or
reducing Mug, a player can
transform him into other Wump
family members.
Zack and Marta experiment with
enlarging and reducing figures on a
coordinate grid. First, Zack draws
Mug Wump on graph paper.
Rule
(Point)
(x, y)
A
(0, 1)
B
(2, 1)
C
(2, 0)
D
(3, 0)
E
(3, 1)
F
(5, 1)
G
(5, 0)
H
Mug Wump
Rule
(Point)
(x, y)
N
(2, 2)
O
(6, 2)
(6, 0)
P
(6, 3)
I
(6, 1)
Q
(2, 3)
J
(8, 1)
R
(2, 2)
K
(6, 7)
L
(2, 7)
M
(0, 1)
START OVER
Yeah!
START OVER
Yeah!
S
(3, 4)
T
(4, 5)
U
(5, 4)
V
(3, 4)
START OVER
W
(2, 5)
(make
a dot)
X
(6, 5)
(make
a dot)
Yeah!
Let’s make the other Wump
family members!
Who do you want to draw first?
Zug
Lug
Bug
Glug
Click here
when the
Wump
family is
complete!
Rule
(Point)
(x, y)
(2x, 2y)
A
(0, 1)
(0, 2)
B
(2, 1)
(4, 2)
C
(2, 0)
(4, 0)
D
(3, 0)
(6, 0)
E
(3, 1)
(6, 2)
F
(5, 1)
(10, 2)
G
(5, 0)
H
(6, 0)
I
(6, 1)
J
(8, 1)
K
(6, 7)
(12, 14)
L
(2, 7)
(4, 14)
M
(0, 1)
(0, 2)
Zug
The rule for Zug is (2x, 2y)
Rule
(Point)
(x, y)
(2x, 2y)
WhichNmeans
(2, 2) that
(4, 4) you must multiply each
(10, 0)
O and
(6, 2)y value
(12, 4)
x
value
in the coordinate pair
(12, 0)
P
(6, 3)
(12, 6)
(12, 2)by 2. This will give you the coordinate
Q
(2, 3)
(4, 6)
Yeah!
(16, 2)
R
(2, 2) pairs
(4, 4) for Zug.
START OVER
Yeah!
START OVER
S
(3, 4)
(6, 8)
T
(4, 5)
U
(5, 4)
(10, 8)
V
(3, 4)
(6, 8)
(8, 10)
GOODLUCK!
START OVER
W
X
(2, 5)
(4, 10)
(make a
dot)
(make a
dot)
(6, 5)
(12, 10)
(make a
dot)
(make a
dot)
Yeah!
Is Zug a member of the Wump
family or is he an imposter?
YES He is a family member!
NO He is an IMPOSTER!
Mug Wump
Zug
Zug IS a member of the
Wump family!
Let’s try
another
family
member!
Mug Wump
Zug Wump
Lug
Rule
(Point)
(x, y)
(3x, y)
A
(0, 1)
(0, 1)
B
(2, 1)
(6, 1)
C
(2, 0)
(6, 0)
D
(3, 0)
(9, 0)
E
(3, 1)
(9, 1)
F
(5, 1)
(15, 1)
G
(5, 0)
H
(6, 0)
I
(6, 1)
J
(8, 1)
K
(6, 7)
L
(2, 7)
WhichN means
that
(2, 2)
(6, 2) you must multiply each
(15, 0)
O
(6, 2)the(18,
2)
x
value
in
coordinate
pair by 3 and
(18, 0)
P
(6, 3)
(18, 3)
y
value
in
the coordinate pair by 1.
(18,each
1)
Q
(2, 3)
(6, 3)
(24,This
1)
Yeah!
will
give
coordinate pairs for
R
(2, 2) you
(6, 2) the
(18, 7) Yeah!
START OVER
Lug.
(6, 7)
M
(0, 1)
(0, 1)
START OVER
The rule for Lug is (3x, y)
Rule
(Point)
(x, y)
(3x, y)
S
(3, 4)
(9, 4)
T
(4, 5)
(12, 5)
U
(5, 4)
V
(3, 4)
(15, 4)
GOODLUCK!
Yeah!
(9, 4)
START OVER
W
X
(2, 5)
(6, 5)
(make a
dot)
(make a
dot)
(6, 5)
(18, 5)
(make a
dot)
(make a
dot)
Is Lug a member of the Wump
family or is he an imposter?
YES He is a family member!
NO He is an IMPOSTER!
Mug Wump
Lug
Lug IS NOT a member of the
Wump family!
Let’s try
another
family
member!
Mug Wump
Lug
Rule
(Point)
(x, y)
(3x, 3y)
A
(0, 1)
(0, 3)
B
(2, 1)
(6, 3)
C
(2, 0)
(6, 0)
D
(3, 0)
(9, 0)
E
(3, 1)
(9, 3)
F
(5, 1)
(15, 3)
G
(5, 0)
H
(6, 0)
I
(6, 1)
J
(8, 1)
K
(6, 7)
L
(2, 7)
M
(0, 1)
Bug
The rule for Bug is (3x, 3y)
Rule
(Point)
(x, y)
(3x, 3y)
WhichN means
that
(2, 2)
(6, 6) you must multiply each
(15, 0)
O
(6, 2) y value
(18, 6)
x
value
and
in the coordinate pair
(18, 0)
P
(6, 3)
(18, 9)
(18, 3)by 3. This will give you the coordinate
Q
(2, 3)
(6, 9)
(24, 3)
Yeah!Bug.
pairs
for
R
(2, 2)
(6, 6)
(18, 21) Yeah!
START OVER
(6, 21)
S
(3, 4)
(9, 12)
(0, 3)
START OVER
T
(4, 5)
(12, 15)
GOODLUCK!
U
(5, 4)
(15, 12)
V
(3, 4)
(9, 12)
START OVER
W
X
(2, 5)
(6, 15)
(make a
dot)
(make a
dot)
(6, 5)
(18, 15)
(make a
dot)
(make a
dot)
Yeah!
Is Bug a member of the Wump
family or is he an imposter?
YES He is a family member!
NO He is an IMPOSTER!
Mug Wump
Bug
Bug IS a member of the
Wump family!
Let’s try
another
family
member!
Mug Wump
Bug Wump
Is Glug a member of the Wump
family or is he an imposter?
YES He is a family member!
NO He is an IMPOSTER!
Glug
Mug Wump
Glug
Rule
(Point)
(x, y)
(x, 3y)
A
(0, 1)
(0, 3)
B
(2, 1)
(2, 3)
C
(2, 0)
(2, 0)
D
(3, 0)
(3, 0)
E
(3, 1)
(3, 3)
F
(5, 1)
G
(5, 0)
H
(6, 0)
I
(6, 1)
J
(8, 1)
K
(6, 7)
L
(2, 7)
WhichN means
that
(2, 2)
(2, 6) you must multiply each
(5, 0)
O
(6, 2)the(6,
6)
x
value
in
coordinate
pair by 1 and
(6, 0)
P
(6, 3)
(6, 9)
eachQ y value
in
the coordinate pair by 3.
(6, 3)
(2, 3)
(2, 9)
(8,This
3)
Yeah!coordinate pairs for
will
give
R
(2, 2) you
(2, 6) the
(6, 21) Yeah!
START OVER
Glug.
(2, 21)
M
(0, 1)
(0, 3)
The rule for Glug is (x, 3y)
Rule
(Point)
(x, y)
(x, 3y)
S
(3, 4)
(3, 12)
T
(4, 5)
(4, 15)
U
(5, 4)
V
(3, 4)
(5, 3)
START OVER
(5, 12)
GOODLUCK!
Yeah!
(3, 12)
START OVER
W
X
(2, 5)
(2, 15)
(make a
dot)
(make a
dot)
(6, 5)
(6, 15)
(make a
dot)
(make a
dot)
Glug IS NOT a member of the
Wump family!
Glug
Let’s try
another
family
member!
Mug Wump
Remember they must have the
same shape. The only
difference can be their size!
Click to
try again
The Wump Family thanks you!
Mug Wump
Bug Wump
Zug Wump