Post on 24-May-2020
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.