Investigation 2.1 Investigation 2.1 Drawing WumpsDrawing Wumps
Stretching & ShrinkingStretching & 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.
Mug WumpMug WumpRuleRule(Point)(Point)
(x, y)(x, y)
AA (0, 1)(0, 1)
BB (2, 1)(2, 1)
CC (2, 0)(2, 0)
DD (3, 0)(3, 0)
EE (3, 1)(3, 1)
FF (5, 1)(5, 1)
GG (5, 0)(5, 0)
HH (6, 0)(6, 0)
II (6, 1)(6, 1)
JJ (8, 1)(8, 1)
KK (6, 7)(6, 7)
LL (2, 7)(2, 7)
MM (0, 1)(0, 1)
START OVERSTART OVER
RuleRule(Point)(Point)
(x, y)(x, y)
NN (2, 2)(2, 2)
OO (6, 2)(6, 2)
PP (6, 3) (6, 3)
QQ (2, 3)(2, 3)
RR (2, 2)(2, 2)
START OVERSTART OVER
SS (3, 4)(3, 4)
TT (4, 5)(4, 5)
UU (5, 4)(5, 4)
VV (3, 4)(3, 4)
START OVERSTART OVER
WW (2, 5) (2, 5) (make (make a dot)a dot)
XX (6, 5) (6, 5) (make (make a dot)a dot)
Yeah!
Yeah!
Yeah!
Let’s make the other Wump Let’s make the other Wump family members!family members!
Who do you want to draw first?Who do you want to draw first?ZugLugBugGlug Click here
when the Wump
family is complete!
ZugZugRuleRule(Point)(Point)
(x, y)(x, y) (2x, 2y)(2x, 2y)
AA (0, 1)(0, 1) (0, 2)(0, 2)
BB (2, 1)(2, 1) (4, 2)(4, 2)
CC (2, 0)(2, 0) (4, 0)(4, 0)
DD (3, 0)(3, 0) (6, 0)(6, 0)
EE (3, 1)(3, 1) (6, 2)(6, 2)
FF (5, 1)(5, 1) (10, 2)(10, 2)
GG (5, 0)(5, 0) (10, 0)(10, 0)
HH (6, 0)(6, 0) (12, 0)(12, 0)
II (6, 1)(6, 1) (12, 2)(12, 2)
JJ (8, 1)(8, 1) (16, 2)(16, 2)
KK (6, 7)(6, 7) (12, 14)(12, 14)
LL (2, 7)(2, 7) (4, 14)(4, 14)
MM (0, 1)(0, 1) (0, 2)(0, 2)
START OVERSTART OVER
RuleRule(Point)(Point)
(x, y)(x, y) (2x, 2y)(2x, 2y)
NN (2, 2)(2, 2) (4, 4)(4, 4)
OO (6, 2)(6, 2) (12, 4)(12, 4)
PP (6, 3) (6, 3) (12, 6)(12, 6)
QQ (2, 3)(2, 3) (4, 6)(4, 6)
RR (2, 2)(2, 2) (4, 4)(4, 4)
START OVERSTART OVER
SS (3, 4)(3, 4) (6, 8)(6, 8)
TT (4, 5)(4, 5) (8, 10)(8, 10)
UU (5, 4)(5, 4) (10, 8)(10, 8)
VV (3, 4)(3, 4) (6, 8)(6, 8)
START OVERSTART OVER
WW (2, 5) (2, 5) (make a (make a
dot)dot)
(4, 10) (4, 10) (make a (make a
dot)dot)
XX (6, 5) (6, 5) (make a (make a
dot)dot)
(12, 10) (12, 10) (make a (make a
dot)dot)
Yeah!
Yeah!
Yeah!
The rule for Zug is (2x, 2y)
Which means that you must multiply each x value and y value in the coordinate pair
by 2. This will give you the coordinate pairs for Zug.
GOODLUCK!
Is Zug a member of the Wump Is Zug a member of the Wump family or is he an imposter?family or is he an imposter?
He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!
Mug Wump
Zug
NO
YES
Zug Zug ISIS a member of the a member of the Wump family!Wump family!
Mug Wump
Zug Wump
Let’s tryanotherfamily
member!
LugLugRuleRule(Point)(Point)
(x, y)(x, y) (3x, y)(3x, y)
AA (0, 1)(0, 1) (0, 1)(0, 1)
BB (2, 1)(2, 1) (6, 1)(6, 1)
CC (2, 0)(2, 0) (6, 0)(6, 0)
DD (3, 0)(3, 0) (9, 0)(9, 0)
EE (3, 1)(3, 1) (9, 1)(9, 1)
FF (5, 1)(5, 1) (15, 1)(15, 1)
GG (5, 0)(5, 0) (15, 0)(15, 0)
HH (6, 0)(6, 0) (18, 0)(18, 0)
II (6, 1)(6, 1) (18, 1)(18, 1)
JJ (8, 1)(8, 1) (24, 1)(24, 1)
KK (6, 7)(6, 7) (18, 7)(18, 7)
LL (2, 7)(2, 7) (6, 7)(6, 7)
MM (0, 1)(0, 1) (0, 1)(0, 1)
START OVERSTART OVER
RuleRule(Point)(Point)
(x, y)(x, y) (3x, y)(3x, y)
NN (2, 2)(2, 2) (6, 2)(6, 2)
OO (6, 2)(6, 2) (18, 2)(18, 2)
PP (6, 3) (6, 3) (18, 3) (18, 3)
QQ (2, 3)(2, 3) (6, 3)(6, 3)
RR (2, 2)(2, 2) (6, 2)(6, 2)
START OVERSTART OVER
SS (3, 4)(3, 4) (9, 4)(9, 4)
TT (4, 5)(4, 5) (12, 5)(12, 5)
UU (5, 4)(5, 4) (15, 4)(15, 4)
VV (3, 4)(3, 4) (9, 4)(9, 4)
START OVERSTART OVER
WW (2, 5) (2, 5) (make a (make a
dot)dot)
(6, 5) (6, 5) (make a (make a
dot)dot)
XX (6, 5) (6, 5) (make a (make a
dot)dot)
(18, 5) (18, 5) (make a (make a
dot)dot)
Yeah!
Yeah!
Yeah!
The rule for Lug is (3x, y)
Which means that you must multiply each x value in the coordinate pair by 3 and
each y value in the coordinate pair by 1. This will give you the coordinate pairs for
Lug.
GOODLUCK!
Is Lug a member of the Wump Is Lug a member of the Wump family or is he an imposter?family or is he an imposter?
He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!
Mug Wump
NO
YES
Lug
Lug Lug IS NOTIS NOT a member of the a member of the Wump family!Wump family!
Mug WumpLet’s tryanotherfamily
member!
Lug
BugBugRuleRule(Point)(Point)
(x, y)(x, y) (3x, 3y)(3x, 3y)
AA (0, 1)(0, 1) (0, 3)(0, 3)
BB (2, 1)(2, 1) (6, 3)(6, 3)
CC (2, 0)(2, 0) (6, 0)(6, 0)
DD (3, 0)(3, 0) (9, 0)(9, 0)
EE (3, 1)(3, 1) (9, 3)(9, 3)
FF (5, 1)(5, 1) (15, 3)(15, 3)
GG (5, 0)(5, 0) (15, 0)(15, 0)
HH (6, 0)(6, 0) (18, 0)(18, 0)
II (6, 1)(6, 1) (18, 3)(18, 3)
JJ (8, 1)(8, 1) (24, 3)(24, 3)
KK (6, 7)(6, 7) (18, 21)(18, 21)
LL (2, 7)(2, 7) (6, 21)(6, 21)
MM (0, 1)(0, 1) (0, 3)(0, 3)
START OVERSTART OVER
RuleRule(Point)(Point)
(x, y)(x, y) (3x, 3y)(3x, 3y)
NN (2, 2)(2, 2) (6, 6)(6, 6)
OO (6, 2)(6, 2) (18, 6)(18, 6)
PP (6, 3) (6, 3) (18, 9) (18, 9)
QQ (2, 3)(2, 3) (6, 9)(6, 9)
RR (2, 2)(2, 2) (6, 6)(6, 6)
START OVERSTART OVER
SS (3, 4)(3, 4) (9, 12)(9, 12)
TT (4, 5)(4, 5) (12, 15)(12, 15)
UU (5, 4)(5, 4) (15, 12)(15, 12)
VV (3, 4)(3, 4) (9, 12)(9, 12)
START OVERSTART OVER
WW (2, 5) (2, 5) (make a (make a
dot)dot)
(6, 15) (6, 15) (make a (make a
dot)dot)
XX (6, 5) (6, 5) (make a (make a
dot)dot)
(18, 15) (18, 15) (make a (make a
dot)dot)
Yeah!
Yeah!
Yeah!
The rule for Bug is (3x, 3y)
Which means that you must multiply each x value and y value in the coordinate pair
by 3. This will give you the coordinate pairs for Bug.
GOODLUCK!
Is Bug a member of the Wump Is Bug a member of the Wump family or is he an imposter?family or is he an imposter?
He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!
Mug Wump
NO
YES
Bug
Bug Bug ISIS a member of the a member of the Wump family!Wump family!
Mug WumpLet’s tryanotherfamily
member! Bug Wump
Is Glug a member of the Wump Is Glug a member of the Wump family or is he an imposter?family or is he an imposter?
He is a family member!He is a family member!He is an IMPOSTER!He is an IMPOSTER!
Mug Wump
NO
YES
Glug
GlugGlugRuleRule(Point)(Point)
(x, y)(x, y) (x, 3y)(x, 3y)
AA (0, 1)(0, 1) (0, 3)(0, 3)
BB (2, 1)(2, 1) (2, 3)(2, 3)
CC (2, 0)(2, 0) (2, 0)(2, 0)
DD (3, 0)(3, 0) (3, 0)(3, 0)
EE (3, 1)(3, 1) (3, 3)(3, 3)
FF (5, 1)(5, 1) (5, 3)(5, 3)
GG (5, 0)(5, 0) (5, 0)(5, 0)
HH (6, 0)(6, 0) (6, 0)(6, 0)
II (6, 1)(6, 1) (6, 3)(6, 3)
JJ (8, 1)(8, 1) (8, 3)(8, 3)
KK (6, 7)(6, 7) (6, 21)(6, 21)
LL (2, 7)(2, 7) (2, 21)(2, 21)
MM (0, 1)(0, 1) (0, 3)(0, 3)
START OVERSTART OVER
RuleRule(Point)(Point)
(x, y)(x, y) (x, 3y)(x, 3y)
NN (2, 2)(2, 2) (2, 6)(2, 6)
OO (6, 2)(6, 2) (6, 6)(6, 6)
PP (6, 3) (6, 3) (6, 9) (6, 9)
QQ (2, 3)(2, 3) (2, 9)(2, 9)
RR (2, 2)(2, 2) (2, 6)(2, 6)
START OVERSTART OVER
SS (3, 4)(3, 4) (3, 12)(3, 12)
TT (4, 5)(4, 5) (4, 15)(4, 15)
UU (5, 4)(5, 4) (5, 12)(5, 12)
VV (3, 4)(3, 4) (3, 12)(3, 12)
START OVERSTART OVER
WW (2, 5) (2, 5) (make a (make a
dot)dot)
(2, 15) (2, 15) (make a (make a
dot)dot)
XX (6, 5) (6, 5) (make a (make a
dot)dot)
(6, 15) (6, 15) (make a (make a
dot)dot)
Yeah!
Yeah!
Yeah!
The rule for Glug is (x, 3y)
Which means that you must multiply each x value in the coordinate pair by 1 and
each y value in the coordinate pair by 3. This will give you the coordinate pairs for
Glug.
GOODLUCK!
Glug Glug IS NOTIS NOT a member of the a member of the Wump family!Wump family!
Mug WumpLet’s tryanotherfamily
member!
Glug
Remember they must have the Remember they must have the same shape. The only same shape. The only
difference can be their size!difference can be their size!Click to try again
The Wump Family thanks you!The Wump Family thanks you!
Mug Wump
Zug Wump
Bug Wump