CHAPTER 4 REVIEW - Transformations

Name: ______________________________ Hour: __________ Date: ______________

SECTION 1: Describe the transformation from the empty P to the shaded P. Then

decide if the transformation is an isometry or not.

1) 2) 3) 4)

SECTION 2: Describe the transformation that would map Dragon B onto each of

the other dragons.

5) Dragon A _____________

6) Dragon C _____________

7) Dragon D _____________

8) Dragon E _____________

9) Dragon F _____________

SECTION 3: Sketch the transformation described in the box.

10) Rotation 180˚ about P 11) Reflection in the dotted line 12) A non-rigid transformation

SECTION 4: Sketch each reflection.

13) 14) 15)

rotation reflection dilation translation YES YES NO YES

reflection translation translation reflection rotation

SECTION 5: Name the image of Shape A after each reflection.

16) Reflection the y-axis. ____________________

17) Reflection in the x-axis. __________________

18) Reflection in the line y = x. _______________

19) Reflection in the line y = -x. _______________

SECTION 6: Use the properties of reflections to determine the coordinates of the

image of each transformation WITHOUT GRAPHING.

20) Point A(4, -10) is reflected in the x-axis. _________________________________

21) Point B(-5, -6) is reflected in the y-axis. __________________________________

22) Point C(-8, 1) is reflected in the x-axis then in the y-axis. ___________________

SECTION 7: Find the value of each variable given that the transformation was a

reflection.

23)

SECTION 8: Determine how many lines of symmetry each figure has. Sketch in

the lines of symmetry.

24) 25) 26) 27)

SECTION 9: Determine if each shape has rotational symmetry. If it does, state the

degrees at which it will be rotationally symmetric.

28) 29) 30) 31)

Shape B Shape D Shape C Shape A

A’(4, 10) B’(5, -6)

C’(8, -1)

a = 46 b = 95 c = 7 d = 3 5

two four none one

60°, 120°, 180° 90°, 180° none 180°

SECTION 10: State the point, segment, or triangle that represents the image of

each transformation.

32) A 90˚ clockwise rotation of C about point I. _______________

33) A 90˚ counterclockwise rotation of ID about the I. _________

34) A 180˚ rotation of ∆AHI about the point I. ________________

35) A 270˚ clockwise rotation of GE about the point G. ________

36) A 90˚ clockwise rotation of ∆EDI about the point D. ________

37) A 90˚ counterclockwise rotation of ∆ACE about I. _________

SECTION 11: Find the value of each

variable given that each

transformation is an isometry.

38)

SECTION 12: What is the angle of

rotation that mapped HJ onto H’’J’’

39)

SECTION 13: State the name of each vector and write its component form.

40) 41) 42)

SECTION 14: Describe each translation in coordinate form and component form.

43) ΔABC ΔJKL _______________________________________

44) ΔDEF ΔGHI ______________________________________

45) ΔMNO ΔABC _____________________________________

46) ΔJKL ΔDEF _______________________________________

point E IB

ΔDIE GA ΔIDC ΔGAC

x = 7 y = 4 z = 17

136°

ST XW GH

‹4, -6› ‹-6, -2› ‹0, -7›

(x, y) (x + 12, y), ‹12, 0› (x, y) (x + 7, y + 4), ‹7, 4› (x, y) (x - 13, y + 11), ‹-13, 11›

(x, y) (x - 13, y - 10), ‹-13, -10›

SECTION 15: Perform the composition of transformations. State the image vertices.

47) Reflection in the x-axis 48) Rotation of 180˚ about origin 49) Translation of ⟨-12, 10⟩

Rotation 90˚ CCW about origin Translation of (x, y) (x – 9, y + 2) Reflection in the line x = -1

IMAGE VERTICES: IMAGE VERTICES: IMAGE VERTICES:

_____________________________ _________________________ _________________________

SECTION 16: Describe the composition of transformations that was performed.

50) 51)

P’

Q’

P’’

Q’’

P’’(7, -2), Q’’(-3, -7) A’’(-4, -6), B’’(-1, -2) C’’(-4, -1), D’’(-7, -2)

R’’(1, 9), S’’(8, 5), T’’(2, 3)

D’ C’ B’

A’

C’’ B’’ D’’

A’’

R’

T’

S’ R’’

S’’ T’’

Rotation of 90° CW about the origin. Reflection in the line x = 1.

Translation of ‹11, 1› or (x, y) (x + 11, y + 1). Rotation of 90° CW about the origin.