Determine the rule described in the transformations below. a) Rigid Transformation/Isometry b) Translations

Transformation Unit Review

Name ____________________________________________ Period ___________ Date:_______________

Determine the rule described in the transformations below.

1. Which transformation has occurred to quadrilateral AHUP?

a. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 90°

b. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑥 − 𝑎𝑥𝑖𝑠

c. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 180°

d. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑦 − 𝑎𝑥𝑖𝑠

2. Which transformation has occurred to triangle UXS?

a. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 90°

b. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑥 − 𝑎𝑥𝑖𝑠

c. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 180°

d. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑦 − 𝑎𝑥𝑖𝑠

3. Which transformation has occurred to quadrilateral AKJI?

a. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑦 = 𝑥

b. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 270°

c. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑥 − 𝑎𝑥𝑖𝑠

d. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 360°

4. Which transformation has occurred to quadrilateral BKHP?

a. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑦 = 𝑥

b. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 270° CCW

c. 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 𝑎𝑐𝑟𝑜𝑠𝑠 𝑥 − 𝑎𝑥𝑖𝑠

d. 𝑟𝑜𝑡𝑎𝑡𝑒𝑑 360°

Find the coordinates of the vertices of each figure after the transformations.

5. What would be the vertices of the image if the pre-image had vertices 𝐴(2, −2), 𝐵(1, 2), 𝐶(3,3), 𝐷(5, 2) and they were

rotated 180° CW about the origin?

a. 𝐴′(2, −2), 𝐵′(−1, 2), 𝐶′(−3,3), 𝐷′(−5, 2)

b. 𝐴′(−2,2), 𝐵′(−1, −2), 𝐶′(−3, −3), 𝐷′(−5, − 2)

c. 𝐴′(−2, −2), 𝐵′(−1, −2), 𝐶′(−3, −3), 𝐷′(−5, 2)

d. 𝐴′(2,2), 𝐵′(−1, − 2), 𝐶′(−3,3), 𝐷′(−5, 2)

6. What would be the vertices of the image if the pre-image had vertices 𝐴(2, −2), 𝐵(1, 2), 𝐶(3,3), 𝐷(5, 2) and they were

reflected across the x-axis?

a. 𝐴′(2, −2), 𝐵′(−1, 2), 𝐶′(−3,3), 𝐷′(−5, 2)

b. 𝐴′(−2,2), 𝐵′(−1, −2), 𝐶′(−3, −3), 𝐷′(−5, − 2)

c. 𝐴′(−2, −2), 𝐵′(−1, −2), 𝐶′(−3, −3), 𝐷′(−5, 2)

d. 𝐴′(2,2), 𝐵′(−1, 2), 𝐶′(3, −3), 𝐷′(5, −2)

7. What would be the vertices of the image if the pre-image had vertices 𝐴(2, −2), 𝐵(1, 2), 𝐶(3,3), 𝐷(5, 2) and they were rotated 270° CCW about the origin?

a. 𝐴′(2, −2), 𝐵′(−1, 2), 𝐶′(−3,3), 𝐷′(−5, 2)

b. 𝐴′(−2,2), 𝐵′(−1, −2), 𝐶′(−3, −3), 𝐷′(−5, − 2)

c. 𝐴′(−2, −2), 𝐵′(2, −1), 𝐶′(3, −3), 𝐷′(2, −5)

d. 𝐴′(2, −2), 𝐵′(2, 1), 𝐶′(3, −3), 𝐷′(2, 5)

8. On the graph to the right draw and label the triangle with vertices 𝐴(−4, 5), 𝐵(3,2), 𝐶(−1,4) after all of the

transformations listed below are done. DRAW all the images.

1. 𝑇𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑒𝑑 2 𝑢𝑛𝑖𝑡 𝑟𝑖𝑔ℎ𝑡 𝑎𝑛𝑑 2 𝑢𝑛𝑖𝑡𝑠 𝑑𝑜𝑤𝑛

2. 𝑅𝑒𝑓𝑙𝑒𝑐𝑡 𝑎𝑐𝑟𝑜𝑠𝑠 𝑦 = 𝑥

3. 𝑅𝑜𝑡𝑎𝑡𝑒 90 𝑑𝑒𝑔𝑟𝑒𝑒𝑠 𝐶𝐶𝑊 𝑎𝑏𝑜𝑢𝑡 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛

Vocabulary review: 9. List important Characteristics of each.

a) Rigid Transformation/Isometry b) Translations

c) Reflections d) Rotations e) Dilations f) Composition for Transformations

10. What is the difference between two figures that are congruent and two figures that are similar?

11. Name the ordered pair rule that transforms each figure into its image. Rule: (x, y)  ______________ Rule: (x, y) _____________ Rule: (x, y) _____________

Complete the following transformations on the figure:

12. Reflect 𝑉𝑈𝑊 across the y-axis, then translate it by the rule (𝑥, 𝑦) → (𝑥 − 3, 𝑦 + 4)

13. Translate 𝐴𝐵𝐶𝐷 by the rule (𝑥, 𝑦) → (𝑥 − 5, 𝑦), then rotate the figure 180°.

14.

Determine the scale factor for the dilations.

15.

a. 𝑘 = 2

b. 𝑘 = 1

c. 𝑘 = 1.5

d. 𝑘 = 0

16.

a. 𝑘 = 2

b. 𝑘 = 1

c. 𝑘 = 0.5

d. 𝑘 = 0

17.

a. 𝑘 = 2 .5

b. 𝑘 = 0.25

c. 𝑘 = 2

d. 𝑘 = 0.50

18.

a. 𝑘 = 0.25

b. 𝑘 = 2

c. 𝑘 = 0.50

d. 𝑘 = 2.5

Determine the coordinate points of the image after the pre-image provided is dilated by the scale factor listed.

19. 𝑘 = 1

2

a. 𝐶’(2,0), 𝑌’(0.5, 0.5), 𝐽’(1.5, 2.5)

b. 𝐶’(1,0), 𝑌’(2.5, 0.5), 𝐽’(1.5, 1.5)

c. 𝐶’(1,0.5), 𝑌’(2.5, 1.5), 𝐽’(2, 1.5)

d. 𝐶’(1,1.5), 𝑌’(2, 0.5), 𝐽’(0.5, 1.5)

20. 𝑘 = 2

a. 𝐷’(−2, 0), 𝑌’(0, 4), 𝑍’(4, −2)

b. 𝐷’(2, 0), 𝑌’(2, −2), 𝑍’(1, −2)

c. 𝐷’(−1, 0), 𝑌’(0, 2), 𝑍’(2, −1)

d. 𝐷’(−2, 2), 𝑌’(2, 4), 𝑍’(0, −2)

21. 𝑘 = 1

4

a. 𝐴’(0.25, 0.5), 𝐿’(2.25, 1.25), 𝑋’(1.75, 1.25)

b. 𝐴’(1.5, 0.25), 𝐿’(1.75, 0.75), 𝑋’(1.75, 0.25)

c. 𝐴’(0.25, 0.5), 𝐿’(1.25, 0.75), 𝑋’(1.25, 1.75)

d. 𝐴’(0.5, 0.25), 𝐿’(1.25, 0.25), 𝑋’(1.25, 0.75)

22. 𝑘 = 1.5

a. 𝐽’(−0.5, −1.5), 𝑋’(0.5, 4.5), 𝐿’(2, 3), 𝑌′(0, 4.5)

b. 𝐽’(−1.5, −1.5), 𝑋’(1.5, 4.5), 𝐿’(3, 3), 𝑌′(0, 4.5)

c. 𝐽’(1.5, 1.5), 𝑋’(1.25, 4.5), 𝐿’(3, 3.5), 𝑌′(0, −4.5)

d. 𝐽’(−2.5, −1.25), 𝑋’(−1.5, 4), 𝐿’(3, −3), 𝑌′(0, 4)

23. Describe the sequences required for the following transformation below:

24. Quadrilateral ABCD is rotated 90 counterclockwise (or 270 clockwise) about the origin. Name the new

coordinates.

Original Coordinates A (1, 3) B (3, 4) C (6, 5) D (1, 5)

New Coordinates

25. Find the Center of Dilation and the Scale Factor for the following:

a)

b)

26. Find the coordinates of the vertices of the figure after a dilation of k = 2 centered at the point (1, -3) and graph the image.

X(______, _______) → X’ (_____, ______)

Y(______, _______) → Y’ (_____, ______)

Z(______, _______) → Z’ (_____, ______)

-14-13-12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

x

y

X

Y

Z

27.

28.