Investigation 2.1 Drawing Wumps Stretching & Shrinking

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