Investigation 2.1 Drawing Wumps Stretching & Shrinking What is a WUMP? Let's find out!

Zach and Marta’s computer game involves a family called the Wumps 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 Wump This is Mug Wump! Yeah! Yeah! Yeah! 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 (6, 0) I (6, 1) J (8, 1) K (6, 7) L (2, 7) M START OVER Rule (Point) (x, y) N (2, 2) O (6, 2) P (6, 3) Q (2, 3) R START OVER S (3, 4) T (4, 5) U (5, 4) V W (2, 5) (make a dot) X (6, 5) (make a dot) This is Mug Wump! Yeah! Yeah! 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!

Zug This is Zug! The rule for Zug is (2x, 2y) (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) (10, 0) H (12, 0) I (6, 1) (12, 2) J (8, 1) (16, 2) K (6, 7) (12, 14) L (2, 7) (4, 14) M START OVER 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! This is Zug! Rule (Point) (x, y) (2x, 2y) N (2, 2) (4, 4) O (6, 2) (12, 4) P (6, 3) (12, 6) Q (2, 3) (4, 6) R START OVER S (3, 4) (6, 8) T (4, 5) (8, 10) U (5, 4) (10, 8) V W (2, 5) (make a dot) (4, 10) (make a dot) X (6, 5) (make a dot) (12, 10) (make a dot) Yeah! Yeah! Yeah!

Is Zug a member of the Wump family or is he an imposter Is Zug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER! YES NO Zug Mug Wump

Zug IS a member of the Wump family! GREAT JOB! but WHY?

but WHY? Zug Wump Mug Wump Let’s try another family member!

Lug This is Lug! The rule for Lug is (3x, y) (Point) (x, y) (3x, y) A (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) (15, 0) H (18, 0) I (18, 1) J (8, 1) (24, 1) K (6, 7) (18, 7) L (2, 7) M START OVER 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! Rule (Point) (x, y) (3x, y) N (2, 2) (6, 2) O (18, 2) P (6, 3) (18, 3) Q (2, 3) R START OVER S (3, 4) (9, 4) T (4, 5) (12, 5) U (5, 4) (15, 4) V W (2, 5) (make a dot) (6, 5) (make a dot) X (18, 5) (make a dot) This is Lug! Yeah! Yeah! Yeah!

Is Lug a member of the Wump family or is he an imposter Is Lug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER! YES NO Mug Wump Lug

Lug IS NOT a member of the Wump family! IMPOSTER!!! but WHY?

but WHY? Mug Wump Lug Let’s try another family member!

Bug This is Bug! The rule for Bug is (3x, 3y) (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) (15, 0) H (18, 0) I (6, 1) (18, 3) J (8, 1) (24, 3) K (6, 7) (18, 21) L (2, 7) (6, 21) M START OVER This is Bug! 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! Rule (Point) (x, y) (3x, 3y) N (2, 2) (6, 6) O (6, 2) (18, 6) P (6, 3) (18, 9) Q (2, 3) (6, 9) R START OVER S (3, 4) (9, 12) T (4, 5) (12, 15) U (5, 4) (15, 12) V W (2, 5) (make a dot) (6, 15) (make a dot) X (6, 5) (make a dot) (18, 15) (make a dot) Yeah! Yeah! Yeah!

Is Bug a member of the Wump family or is he an imposter Is Bug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER! YES NO Bug Mug Wump

Bug IS a member of the Wump family! GREAT JOB! but WHY?

but WHY? Bug Wump Mug Wump Let’s try another family member!

Is Glug a member of the Wump family or is he an imposter Is Glug a member of the Wump family or is he an imposter? He is a family member! He is an IMPOSTER! YES NO Mug Wump Glug

The rule for Glug is (x, 3y) (Point) (x, y) (x, 3y) A (0, 1) (0, 3) B (2, 1) (2, 3) C (2, 0) D (3, 0) E (3, 1) (3, 3) F (5, 1) (5, 3) G (5, 0) H (6, 0) I (6, 1) (6, 3) J (8, 1) (8, 3) K (6, 7) (6, 21) L (2, 7) (2, 21) M START OVER This is Glug! 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! Rule (Point) (x, y) (x, 3y) N (2, 2) (2, 6) O (6, 2) (6, 6) P (6, 3) (6, 9) Q (2, 3) (2, 9) R START OVER S (3, 4) (3, 12) T (4, 5) (4, 15) U (5, 4) (5, 12) V W (2, 5) (make a dot) (2, 15) (make a dot) X (6, 5) (make a dot) (6, 15) (make a dot) Yeah! Yeah! Yeah!

Glug IS NOT a member of the Wump family! IMPOSTER!!! but WHY?

but WHY? Mug Wump Glug Let’s try another family member!

Look at those again! 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

(4x,3y) Would this rule create a Wump or an imposter? How would the rule change Mug?

(2x,2y) Would this rule create a Wump or an imposter? How would the rule change Mug?

(1.5x,1.5y) Would this rule create a Wump or an imposter? How would the rule change Mug?

(3x,y) Would this rule create a Wump or an imposter? How would the rule change Mug?