Name: ________________________ Class: ___________________ Date: __________
Unit 5 - Test Study Guide
____
1. Which of these transformations appear to be a rigid motion?
(I) parallelogram EFGH → parallelogram XWVU
(II) hexagon CDEFGH → hexagon YXWVUT
(III) triangle EFG → triangle VWU
A. I only
B. II and III only
C. I and II only
D. I, II, and III
In the diagram, figure RQTS is the image of figure DEFC after a rigid motion.
____
____
2. Name the image of ∠F.
A. ∠T
B. ∠R
C. ∠Q
D. ∠S
3. Name the image of FC .
B. ST
A. TQ
C. RS
D. QR
1
ID: A
Name: ________________________
____
ID: A
4. Which graph shows T < −3,3 > ( ABC) ?
A.
C.
B.
D.
2
Name: ________________________
____
ID: A
5. Which graph shows T < −4,2 > ( ABC)?
A.
C.
B.
D.
3
Name: ________________________
ID: A
Use the diagram.
____
6. Find the image of C under the translation described by the translation rule T < 4,5 > (C).
A. B
B. E
C. A
D. D
____
7. Find the translation rule that describes the translation B → E.
A. T < 8,14 > (B)
C. T < − 4,10 > (A)
B. T < 0,15 > (B)
D. T < 7,2 > (B)
____
8. The vertices of a rectangle are R(–5, –5), S(–1, –5), T(–1, 1), and U(–5, 1). A translation maps R to the point
(–4, 2). Find the translation rule and the image of U.
A. T < −1,7 > (RSTU); (−6, 8)
B. T < 1,7 > (RSTU); (−4, 8)
C. T < 1,−7 > (RSTU); (−4, − 6)
D. T < −1,−7 > (RSTU); (−6, − 6)
____
9. Describe in words the translation of X represented by the translation rule T < −2,8 > (X).
A. 2 units to the left and 8 units up
B. 2 units to the right and 8 units down
C. 8 units to the left and 2 units down
D. 2 units to the right and 8 units up
____ 10. Use a translation rule to describe the translation of X that is 5 units to the left and 7 units up.
C. T < −5,−7 > (X)
A. T < 5,7 > (X)
B. T < −5,7 > (X)
D. T < 5,−7 > (X)
4
Name: ________________________
ID: A
____ 11. Jessica was sitting in row 9, seat 3 at a soccer game when she discovered her ticket was for row 1, seat 1.
Write a rule to describe the translation needed to put her in the proper seat.
C. T <-8,-2> (Jessica)
A. T <-8,2> (Jessica)
B. T <8,2> (Jessica)
D. T <8,-2> (Jessica)
____ 12. Use a translation rule to describe the translation of P that is 6 units to the left and 6 units down.
C. T < −6,−6 > (P)
A. T < 6,6 > (P)
B. T < −6,6 > (P)
D. T < 6,−6 > (P)
____ 13. What is a rule that describes the translation ABCD → A′B ′C ′D ′?
A. T < 3,−2 > (ABCD)
B. T < 3,2 > (ABCD)
C. T < 2,−3 > (ABCD)
D. T < −3,2 > (ABCD)
____ 14. Use a translation rule to describe the translation of ABC that is 8 units to the right and 2 units down.
C. T < −8,2 > ( ABC)
A. T < 8,2 > ( ABC)
B. T < −8,−2 > ( ABC)
D. T < 8,−2 > ( ABC)
____ 15. What translation rule can be used to describe the result of the composition of
T < −5,−3 > (x,y) and T < −7,−1 > (x,y)?
A. T < 12,−4 > (x,y)
B. T < −12,−4 > (x,y)
C. T < −4,−12 > (x,y)
D. T < 2,−2 > (x,y)
5
Name: ________________________
ID: A
16. In the diagram, the dashed-lined figure is the image of the solid-lined figure after a rigid motion.
a. List all pairs of corresponding sides.
b. Name the image of point C .
17. What are the vertices of T < 2,2 > (∆ABC)? Graph T < 2,2 > (∆ABC).
18. Megan left her house and walked 5 blocks north and 4 blocks east to a friend’s house. From there, she walked
5 blocks north and 6 blocks west to school for volleyball practice.
a. If Megan’s house is at the origin, sketch the transformations of her route.
b. Describe where the school is in relation to Megan’s house in words and using function notation.
____ 19. Write a rule in function notation to describe the transformation that is a reflection across the y-axis.
A. R y = x (x,y)
C. R y = 0 (x,y)
B. R x = 0 (x,y)
D. R x = −1 (x,y)
____ 20. The vertices of a triangle are P(–8, 6), Q(1, –3), and R(–6, –3). Name the vertices of R y = x ( PQR) .
C. P ′(−6, 8), Q ′(3, − 1), R ′( 3,6)
A. P ′(−6, − 8), Q ′(3, 1), R ′(3, − 6)
B. P ′(6, − 8), Q ′(−3, 1), R ′(−3, − 6)
D. P ′(6, 8), Q ′(−3, − 1), R ′(−3, 6)
6
Name: ________________________
ID: A
____ 21. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of R y = 0 ( PQR) .
A. P ′(3, 8), Q ′(6, − 4), R ′(−1, 1)
C. P ′(−3, − 8), Q ′(−6, 4), R ′(1, − 1)
B. P ′(−3, 8), Q ′(−6, − 4), R ′(1, 1)
D. P ′(3, − 8), Q ′(6, 4), R ′(−1, − 1)
____ 22. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of R x = 0 ( PQR) .
C. P ′(2, − 4), Q ′(−2, − 5), R ′(1, − 8)
A. P ′(−2, − 4), Q ′(2,− 5), R ′(−1,− 8)
′
′
′
B. P (−2,4), Q (2,5), R (−1,8)
D. P ′(2, 4), Q ′(−2, 5), R ′(1, 8)
____ 23. Write a rule in function notation to describe the transformation that is a reflection across the x-axis.
C. R x = 0 (x,y)
A. R y = x (x,y)
B. R x = y (x,y)
D. R y = 0 (x,y)
____ 24. Find the image of P(–2, –1) after two reflections; first R y = −5 (P) , and then R x = 1 (P' ) .
A. (–2, –1)
B. (–1, –6)
C. (4, –9)
7
D. (1, –5)
Name: ________________________
ID: A
____ 25. Which graph shows a triangle and its reflection image over the x-axis?
C.
A.
B.
D.
8
Name: ________________________
ID: A
____ 26. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you
describe Triangle 3 by using a reflection rule?
A. R m (Triangle 2)
C. R l (Triangle 1)
B. R m (Triangle 1)
D. R l (Triangle 2)
____ 27. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you
describe Triangle 2 by using a reflection rule?
I. R l (Triangle 3)
II. R m (Triangle 2)
III. R m (Triangle 1)
A. I only
C. II and III only
B. I and III only
D. I, II, and III
9
Name: ________________________
ID: A
28. Draw R x-axis (∆ABC).
29. Graph points A(1, 5), B(5, 2), and C(1, 2). Graph R y = 0 ( ABC) .
30. In the figure, A′B ′ = R k (AB) .
a. Find and name two points that line k passes through.
b. Explain how you know that line k passes through those two points.
c. Graph line k and the point C(3, –2) and show its image as a reflection across line k.
10
Name: ________________________
ID: A
The hexagon GIKMPR and ∆FJN are regular. The dashed line segments form 30° angles.
____ 31. What is r (240 °, O ) (G)?
A. P
B. I
C. K
D. O
B. OF
C. OL
D. OH
____ 32. Find r (120°,O) (OL).
A. OJ
____ 33. A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the
coordinates of the first car after a rotation of 270° about the origin?
A. (−30,0)
B. (0,−30)
C. (0,30)
D. (−15,−15)
34. a. Graph the quadrilateral WXYZ with vertices W(3, –5), X(1, –3), Y(–1, –5), and Z(1, –7).
b. Graph r (90°,O) (WXYZ) and state the coordinates of the vertices.
____ 35. Which type of isometry is the equivalent of two reflections across intersecting lines?
A. glide reflection
C. reflection
B. rotation
D. none of these
____ 36. The glide reflection R y = −x û T < 4,1 > maps the point P to (4, 3). Find the coordinates of P.
A. (–2, 0)
B. (1, –3)
C. (0, 2)
11
D. (–8, –4)
Name: ________________________
ID: A
37. Find (R m û R l )(D).
38. Find (R n û R m û R l )(P).
12
Name: ________________________
ID: A
39. Find (R m û R l )(B).
40.
a. Graph A′B ′ = R y = x (AB).
b. Graph A″B ″ = (R y = 0 û T < −8,0 > )(AB).
c. Describe a single rigid motion that produces the isometry in part ( b).
41. Suppose R m (3, −4) = (1,1) and R n (1,1) = (−5,16) . Is m || n? Explain.
13
Name: ________________________
ID: A
____ 42. Find the glide reflection image of the black triangle for the composition (R x = 1 û T < 0,−7 > ).
A.
C.
B.
D.
Use the composition (R l û r (−− 90, C ′) )( ABC) =
____ 43. Which angle has an equal measure to m∠B?
A. m∠D
B. m∠A
DEF , shown below.
C. m∠F
D. m∠E
14
Name: ________________________
ID: A
____ 44. Which angle has an equal measure to m∠C ?
A. m∠D
B. m∠A
C. m∠F
D. m∠E
____ 45. Which side has an equal measure to BC ?
A. DE
B. AB
C. EF
D. DF
Use the figures below.
____ 46. Write a sequence of rigid motions that maps
A. (RST û r (270°,P) )( RST) = ( DEF)
B. R y = x ( RST) = ( DEF)
RST to DEF .
C. r (180°,P) ( RST) = ( DEF)
D. (R y = x û r (180°,P) )( RST) = ( DEF)
____ 47. Write a sequence of rigid motions that maps AB to XY .
A. R x = 0 (AB) = (XY )
C. (T < −1,0 > û r (90°,P) )(AB) = (XY)
B. (R y = x û r (90°,P) )(AB) = (XY)
D. (T < 0,−1 > û r (90°,P) )(AB) = (XY)
15
Name: ________________________
____ 48. In the diagram, ABC ≅
ABC onto LMN ?
ID: A
LMN . What is a congruence transformation that maps
A. (R y = −x )( ABC) = (
LMN)
B. (r (90°,O) û R y = −x )( ABC) = ( LMN)
C. (R y = x û T < 0,−2 > )( ABC) = ( LMN)
D. (R y = −x û T < 0,2 > )( ABC) = ( LMN)
____ 49. Which figures are congruent?
A. B ≅ D and A ≅ C
B. B ≅ D
C. B ≅ D and E ≅ F
D. B ≅ D and E ≅ F and A ≅ C
16
Name: ________________________
ID: A
____ 50. The dashed-lined figure is a dilation image of EFGH. Is D (n,H) an enlargement or a reduction? What is the
scale factor n of the dilation?
A. n = 6; enlargement
C. n = 3; reduction
1
D. n = ; reduction
3
B. n = 3; enlargement
____ 51. The dashed-lined figure is a dilation image of
ABC with center of dilation P (not shown). Is D (n,P) an
enlargement, or a reduction? What is the scale factor n of the dilation?
A. reduction;
n=2
B. reduction;
1
n=
4
C. enlargement;
n=2
D.
reduction;
1
n=
2
____ 52. A blueprint for a house has a scale factor n = 45. A wall in the blueprint is 9 in. What is the length of the
actual wall?
A. 4,860 feet
B. 33.75 in.
C. 405 feet
D. 33.75 feet
17
Name: ________________________
ID: A
____ 53. A microscope shows you an image of an object that is 140 times the object’s actual size. So the scale factor
of the enlargement is 140. An insect has a body length of 6 millimeters. What is the body length of the insect
under the microscope?
A. 840 centimeters
C. 84 millimeters
B. 8,400 millimeters
D. 840 millimeters
____ 54. The zoom feature on a camera lens allows you dilate what appears on the display. When you change from
100% to 500%, the new image on your screen is an enlargement of the previous image with a scale factor of
5. If the new image is 47.5 millimeters wide, what was the width of the previous image?
A. 9.5 millimeters
C. 118.75 millimeters
B. 23.75 millimeters
D. 237.5 millimeters
55. The endpoints of AB are A(9, 4) and B(5, –4). The endpoints of its image after a dilation are A′(6, 3) and
B ′(3, − 3).
a. Explain how to find the scale factor.
b. Locate the center of dilation. Show your work.
56. What are the vertices of ∆ABC for D 2 ( ABC) ? Graph D 2 ( ABC) .
18
Name: ________________________
ID: A
57. What are the images of the vertices of ∆ABC when you apply the composition D(0.5,O) û Rx = 4 ? Graph
(D(0.5,O) û Rx = 4 )( ABC).
58. ∆ABC has vertices A(0,0), B(5,−1) , and C(3,7). What are the vertices of the resulting image when the
triangle is translated 4 units to the left then dilated by a scale factor of 2?
____ 59. What composition of rigid motions and a dilation maps EFGH to the dashed figure?
A. D (3,(2,−2)) û T < 4,−1 >
C. D (3,(2,−2)) û T < −4,1 >
B. D ( 1 ,(2,−2)) û T < 4,−1 >
D. D ( 1 ,(2,−2)) û T < −4,1 >
3
3
60. You have a 5” by 7” photo that you would like to have enlarged to fit an 8” by 10” frame. Would the two
photographs be similar? Explain.
19
ID: A
Unit 5 - Test Study Guide
Answer Section
1. ANS:
NAT:
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2. ANS:
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3. ANS:
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4. ANS:
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9. ANS:
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10. ANS:
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11. ANS:
NAT:
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KEY:
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 1 Identifying an Isometry
transformation | rigid motion
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 2 Naming Images and Corresponding Parts
image | preimage | rigid motion
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 2 Naming Images and Corresponding Parts
image | preimage | corresponding parts | rigid motion
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
translation | transformation | image | preimage
A
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
translation | transformation | preimage | image
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
translation | preimage | image
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation | preimage | image
B
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation | image | preimage
A
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation
C
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation | word problem
1
ID: A
12. ANS: C
PTS: 1
DIF: L3
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
KEY: translation
13. ANS: D
PTS: 1
DIF: L3
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
KEY: translation
14. ANS: D
PTS: 1
DIF: L3
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
KEY: translation
15. ANS: B
PTS: 1
DIF: L4
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 5 Composing Translations
KEY: translation
16. ANS:
a. AB ≅ MN , BC ≅ NJ , CD ≅ JK , DE ≅ KL , EA ≅ LM
b. J
PTS: 1
DIF: L4
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 2 Naming Images and Corresponding Parts
KEY: transformation | image | preimage | multi-part question | rigid motion
17. ANS:
T < 2,2 > (A) = (−6 + 2, 2 + 2) → A′(−4, 4)
T < 2,2 > (B) = (−2 + 2, 4 + 2) → B ′(0, 6)
T < 2,2 > (C) = (−4 + 2, − 4 + 2) → C ′(−2, − 2)
PTS:
NAT:
STA:
KEY:
1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
transformation | image | preimage | translation
2
ID: A
18. ANS:
a.
b. The school is 10 blocks north and 2 block west of Megan’s house.
School = T < −2,10 > (Megan’s house)
19.
20.
21.
22.
23.
24.
PTS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 5 Composing Translations
problem solving | multi-part question | transformation | translation | word problem
B
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
D
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
C
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
3
ID: A
25. ANS:
NAT:
STA:
KEY:
26. ANS:
NAT:
STA:
KEY:
27. ANS:
NAT:
STA:
KEY:
28. ANS:
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | line of reflection
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 3 Writing a Reflection Rule
reflection | line of reflection
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 3 Writing a Reflection Rule
reflection | line of reflection
PTS:
NAT:
STA:
KEY:
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | image | preimage | line of reflection
4
ID: A
29. ANS:
PTS:
NAT:
STA:
KEY:
30. ANS:
[4]
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | image | preimage | line of reflection
a. Answers may vary. Sample: (0, –2) and (2, 0)
b. The line that contains the two points is the perpendicular bisector of AA′ and BB ′ .
c.
[3]
[2]
[1]
error in calculation of one coordinate of the two points on the line of reflection
only two parts correct
only one part correct
PTS:
NAT:
STA:
KEY:
1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | reflection line | extended response | rubric-based question
5
ID: A
31. ANS:
NAT:
STA:
KEY:
32. ANS:
NAT:
STA:
KEY:
33. ANS:
NAT:
STA:
KEY:
34. ANS:
a–b.
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | center of rotation | angle of rotation
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | center of rotation | angle of rotation
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | center of rotation | angle of rotation
Vertices: W ′(5,3), X ′(3,1), Y ′(5,−1), Z ′(7,1)
PTS:
NAT:
STA:
KEY:
35. ANS:
NAT:
TOP:
36. ANS:
NAT:
TOP:
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | angle of rotation | center of rotation
B
PTS: 1
DIF: L2
CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
9-4 Problem 2 Reflections Across Intersecting Lines
KEY: isometry
A
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
9-4 Problem 3 Finding a Glide Reflection Image
KEY: glide reflection | isometry
6
ID: A
37. ANS:
PTS: 1
STA: NC 3.01
KEY: isometry
38. ANS:
DIF: L3
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines
PTS: 1
STA: NC 3.01
KEY: isometry
DIF: L4
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines
7
ID: A
39. ANS:
PTS:
STA:
KEY:
40. ANS:
[4]
1
NC 3.01
isometry
DIF: L3
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
TOP: 9-4 Problem 2 Reflections Across Intersecting Lines
a-b.
c. r (180°, O ) ( AB), a rotation of 180° about the origin
[3]
[2]
[1]
description of isometry missing
correct coordinates named without graphs
only two parts correct
PTS: 1
DIF: L4
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
TOP: 9-4 Problem 3 Finding a Glide Reflection Image
KEY: isometry | glide reflection | extended response | rubric-based question | rigid motion
8
ID: A
41. ANS:
Yes. The reflection lines do not intersect because the three points lie on the same line. Because the line of
reflection is the perpendicular bisector of the segment connecting a point and its image, both lines of
reflection are perpendicular to the line that passes through all three points. Since both lines of reflection are
perpendicular to the same line, they are parallel.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
PTS:
STA:
KEY:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
KEY:
ANS:
NAT:
TOP:
KEY:
ANS:
STA:
KEY:
ANS:
STA:
KEY:
ANS:
STA:
KEY:
ANS:
STA:
KEY:
1
DIF: L4
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
NC 3.01
TOP: 9-4 Problem 1 Reflections Across Parallel Lines
isometry | writing in math | reasoning
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
9-4 Problem 3 Finding a Glide Reflection Image
KEY: isometry | glide reflection
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 1 Identifying Equal Measures
D
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 1 Identifying Equal Measures
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 1 Identifying Equal Measures
A
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 2 Identifying Congruent Figures
KEY: congruent | rigid motion
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 2 Identifying Congruent Figures
KEY: congruent | rigid motion
D
PTS: 1
DIF: L4
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 3 Identifying Congruence Transformations
congruent | congruence transformation
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 5 Determining Congruence
congruent | congruence transformation
B
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 1 Finding a Scale Factor
dilation | enlargement | scale factor
D
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 1 Finding a Scale Factor
dilation | reduction | scale factor
D
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length
dilation | enlargement | scale factor | word problem
D
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length
dilation | enlargement | scale factor | word problem
9
ID: A
54. ANS: A
PTS: 1
DIF: L4
NAT: CC G.CO.2| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length
KEY: dilation | enlargement | scale factor | word problem
55. ANS:
a. Find the length of each segment. Then divide the length of the image by the length of the preimage.
AB =
A′B ′ =
(9 − 5) 2 + (4 − (−4)) 2 = 4 5
(6 − 3) 2 + (3 − (−3)) 2 = 3 5
The scale factor is
3 5
4 5
3
, or .
4
b.
The center is (–3, 0).
PTS: 1
DIF: L4
NAT: CC G.CO.2| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-6 Problem 1 Finding a Scale Factor
KEY: multi-part question | dilation | reduction | center of dilation | scale factor | coordinate plane | graphing
10
ID: A
56. ANS:
D 2 (A) = ((2) ⋅ (−2),(2) ⋅ (4)), or A′(−4,8)
D 2 (B) = ((2) ⋅ (4),(2) ⋅ (2)), or B ′(8,4)
D 2 (C) = ((2) ⋅ (−4),(2) ⋅ (−4)), or C ′(−8,−8)
PTS: 1
DIF: L4
NAT: CC G.CO.2| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-6 Problem 2 Finding a Dilation Image
KEY: dilation | reduction | center of dilation | scale factor | coordinate plane | graphing
57. ANS:
A″ = (5,2)
B ″ = (2,1)
C ″ = (6,−2)
PTS: 1
STA: NC 3.01
DIF: L3
NAT: CC G.SRT.2| CC G.SRT.3
TOP: 9-7 Problem 1 Drawing Transformations
11
ID: A
58. ANS:
T < −4,0 > (A) = (0 − 4,0) = A′(−4,0)
T < −4,0 > (B) = (5 − 4, −1) = B ′(1, −1)
T < −4,0 > (C) = (3 − 4,7) = C ′(−1,7)
D 2 (A′) = (2 ⋅ (−4),2 ⋅ 0) = A″(−8,0)
D 2 (B ′) = (2 ⋅ 1,2 ⋅ (−1)) = B ″(2, −2)
D 2 (C ′) = (2 ⋅ (−1),2 ⋅ 7) = C ″(−2,14)
PTS: 1
DIF: L3
NAT: CC G.SRT.2| CC G.SRT.3
STA: NC 3.01
TOP: 9-7 Problem 1 Drawing Transformations
59. ANS: A
PTS: 1
DIF: L4
NAT: CC G.SRT.2| CC G.SRT.3
STA: NC 3.01
TOP: 9-7 Problem 2 Describing Transformations
KEY: similar | similarity transformation | rigid motion
60. ANS:
No, the two photographs would not be similar. In order for them to be similar, all measurements would have
to be multiplied by the same scale factor.
PTS: 1
DIF: L2
NAT: CC G.SRT.2| CC G.SRT.3
STA: NC 3.01
TOP: 9-7 Problem 4 Determining Similarity
KEY: similarity | similarity transformation
12
Name: ________________________ Class: ___________________ Date: __________
Unit 5 - Test Study Guide
____
1. Which of these transformations appear to be a rigid motion?
(I) parallelogram EFGH → parallelogram XWVU
(II) hexagon CDEFGH → hexagon YXWVUT
(III) triangle EFG → triangle VWU
A. I only
B. II and III only
C. I and II only
D. I, II, and III
In the diagram, figure RQTS is the image of figure DEFC after a rigid motion.
____
____
2. Name the image of ∠F.
A. ∠T
B. ∠R
C. ∠Q
D. ∠S
3. Name the image of FC .
B. ST
A. TQ
C. RS
D. QR
1
ID: A
Name: ________________________
____
ID: A
4. Which graph shows T < −3,3 > ( ABC) ?
A.
C.
B.
D.
2
Name: ________________________
____
ID: A
5. Which graph shows T < −4,2 > ( ABC)?
A.
C.
B.
D.
3
Name: ________________________
ID: A
Use the diagram.
____
6. Find the image of C under the translation described by the translation rule T < 4,5 > (C).
A. B
B. E
C. A
D. D
____
7. Find the translation rule that describes the translation B → E.
A. T < 8,14 > (B)
C. T < − 4,10 > (A)
B. T < 0,15 > (B)
D. T < 7,2 > (B)
____
8. The vertices of a rectangle are R(–5, –5), S(–1, –5), T(–1, 1), and U(–5, 1). A translation maps R to the point
(–4, 2). Find the translation rule and the image of U.
A. T < −1,7 > (RSTU); (−6, 8)
B. T < 1,7 > (RSTU); (−4, 8)
C. T < 1, −7 > (RSTU); (−4, − 6)
D. T < −1, −7 > (RSTU); (−6, − 6)
____
9. Describe in words the translation of X represented by the translation rule T < −2,8 > (X).
A. 2 units to the left and 8 units up
B. 2 units to the right and 8 units down
C. 8 units to the left and 2 units down
D. 2 units to the right and 8 units up
____ 10. Use a translation rule to describe the translation of X that is 5 units to the left and 7 units up.
C. T < −5, −7 > (X)
A. T < 5,7 > (X)
B. T < −5,7 > (X)
D. T < 5, −7 > (X)
4
Name: ________________________
ID: A
____ 11. Jessica was sitting in row 9, seat 3 at a soccer game when she discovered her ticket was for row 1, seat 1.
Write a rule to describe the translation needed to put her in the proper seat.
C. T <-8,-2> (Jessica)
A. T <-8,2> (Jessica)
B. T <8,2> (Jessica)
D. T <8,-2> (Jessica)
____ 12. Use a translation rule to describe the translation of P that is 6 units to the left and 6 units down.
C. T < −6, −6 > (P)
A. T < 6,6 > (P)
B. T < −6,6 > (P)
D. T < 6, −6 > (P)
____ 13. What is a rule that describes the translation ABCD → A′B ′C ′D ′?
A. T < 3, −2 > (ABCD)
B. T < 3,2 > (ABCD)
C. T < 2, −3 > (ABCD)
D. T < −3,2 > (ABCD)
____ 14. Use a translation rule to describe the translation of ABC that is 8 units to the right and 2 units down.
C. T < −8,2 > ( ABC)
A. T < 8,2 > ( ABC)
B. T < −8, −2 > ( ABC)
D. T < 8, −2 > ( ABC)
____ 15. What translation rule can be used to describe the result of the composition of
T < −5, −3 > (x,y) and T < −7, −1 > (x,y)?
A. T < 12, −4 > (x,y)
B. T < −12, −4 > (x,y)
C. T < −4, −12 > (x,y)
D. T < 2, −2 > (x,y)
5
Name: ________________________
ID: A
16. In the diagram, the dashed-lined figure is the image of the solid-lined figure after a rigid motion.
a. List all pairs of corresponding sides.
b. Name the image of point C .
17. What are the vertices of T < 2,2 > (∆ABC)? Graph T < 2,2 > (∆ABC).
18. Megan left her house and walked 5 blocks north and 4 blocks east to a friend’s house. From there, she walked
5 blocks north and 6 blocks west to school for volleyball practice.
a. If Megan’s house is at the origin, sketch the transformations of her route.
b. Describe where the school is in relation to Megan’s house in words and using function notation.
____ 19. Write a rule in function notation to describe the transformation that is a reflection across the y-axis.
A. R y = x (x,y)
C. R y = 0 (x,y)
B. R x = 0 (x,y)
D. R x = −1 (x,y)
____ 20. The vertices of a triangle are P(–8, 6), Q(1, –3), and R(–6, –3). Name the vertices of R y = x ( PQR) .
C. P ′(−6, 8), Q ′(3, − 1), R ′( 3,6)
A. P ′(−6, − 8), Q ′(3, 1), R ′(3, − 6)
B. P ′(6, − 8), Q ′(−3, 1), R ′(−3, − 6)
D. P ′(6, 8), Q ′(−3, − 1), R ′(−3, 6)
6
Name: ________________________
ID: A
____ 21. The vertices of a triangle are P(–3, 8), Q(–6, –4), and R(1, 1). Name the vertices of R y = 0 ( PQR) .
A. P ′(3, 8), Q ′(6, − 4), R ′(−1, 1)
C. P ′(−3, − 8), Q ′(−6, 4), R ′(1, − 1)
B. P ′(−3, 8), Q ′(−6, − 4), R ′(1, 1)
D. P ′(3, − 8), Q ′(6, 4), R ′(−1, − 1)
____ 22. The vertices of a triangle are P(–2, –4), Q(2, –5), and R(–1, –8). Name the vertices of R x = 0 ( PQR) .
C. P ′(2, − 4), Q ′(−2, − 5), R ′(1, − 8)
A. P ′(−2, − 4), Q ′(2,− 5), R ′(−1,− 8)
′
′
′
B. P (−2,4), Q (2,5), R (−1,8)
D. P ′(2, 4), Q ′(−2, 5), R ′(1, 8)
____ 23. Write a rule in function notation to describe the transformation that is a reflection across the x-axis.
C. R x = 0 (x,y)
A. R y = x (x,y)
B. R x = y (x,y)
D. R y = 0 (x,y)
____ 24. Find the image of P(–2, –1) after two reflections; first R y = −5 (P) , and then R x = 1 (P' ) .
A. (–2, –1)
B. (–1, –6)
C. (4, –9)
7
D. (1, –5)
Name: ________________________
ID: A
____ 25. Which graph shows a triangle and its reflection image over the x-axis?
C.
A.
B.
D.
8
Name: ________________________
ID: A
____ 26. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you
describe Triangle 3 by using a reflection rule?
A. R m (Triangle 2)
C. R l (Triangle 1)
B. R m (Triangle 1)
D. R l (Triangle 2)
____ 27. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you
describe Triangle 2 by using a reflection rule?
I. R l (Triangle 3)
II. R m (Triangle 2)
III. R m (Triangle 1)
A. I only
C. II and III only
B. I and III only
D. I, II, and III
9
Name: ________________________
ID: A
28. Draw R x-axis (∆ABC).
29. Graph points A(1, 5), B(5, 2), and C(1, 2). Graph R y = 0 ( ABC) .
30. In the figure, A′B ′ = R k ( AB) .
a. Find and name two points that line k passes through.
b. Explain how you know that line k passes through those two points.
c. Graph line k and the point C(3, –2) and show its image as a reflection across line k.
10
Name: ________________________
ID: A
The hexagon GIKMPR and ∆FJN are regular. The dashed line segments form 30° angles.
____ 31. What is r (240 °, O ) (G)?
A. P
B. I
C. K
D. O
B. OF
C. OL
D. OH
____ 32. Find r (120 °, O ) (OL).
A. OJ
____ 33. A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the
coordinates of the first car after a rotation of 270° about the origin?
A. (−30,0)
B. (0,−30)
C. (0,30)
D. (−15,−15)
34. a. Graph the quadrilateral WXYZ with vertices W(3, –5), X(1, –3), Y(–1, –5), and Z(1, –7).
b. Graph r (90 °, O ) (WXYZ) and state the coordinates of the vertices.
____ 35. Which type of isometry is the equivalent of two reflections across intersecting lines?
A. glide reflection
C. reflection
B. rotation
D. none of these
____ 36. The glide reflection R y = −x û T < 4,1 > maps the point P to (4, 3). Find the coordinates of P.
A. (–2, 0)
B. (1, –3)
C. (0, 2)
11
D. (–8, –4)
Name: ________________________
ID: A
37. Find (R m û R l )(D).
38. Find (R n û R m û R l )(P).
12
Name: ________________________
ID: A
39. Find (R m û R l )(B).
40.
a. Graph A′B ′ = R y = x (AB).
b. Graph A″B ″ = (R y = 0 û T < −8,0 > )(AB).
c. Describe a single rigid motion that produces the isometry in part ( b).
41. Suppose R m (3,−4) = (1,1) and R n (1,1) = (−5,16) . Is m || n? Explain.
13
Name: ________________________
ID: A
____ 42. Find the glide reflection image of the black triangle for the composition (R x = 1 û T < 0, −7 > ).
A.
C.
B.
D.
Use the composition (R l û r (−− 90, C ′) )( ABC) =
____ 43. Which angle has an equal measure to m∠B?
A. m∠D
B. m∠A
DEF , shown below.
C. m∠F
D. m∠E
14
Name: ________________________
ID: A
____ 44. Which angle has an equal measure to m∠C ?
A. m∠D
B. m∠A
C. m∠F
D. m∠E
____ 45. Which side has an equal measure to BC ?
A. DE
B. AB
C. EF
D. DF
Use the figures below.
____ 46. Write a sequence of rigid motions that maps
A. (RST û r (270 °, P ) )( RST) = ( DEF)
B. R y = x ( RST) = ( DEF)
RST to DEF .
C. r (180 °, P ) ( RST) = ( DEF)
D. (R y = x û r (180 °, P ) )( RST) = ( DEF)
____ 47. Write a sequence of rigid motions that maps AB to XY .
A. R x = 0 (AB) = (XY )
C. (T < −1,0 > û r (90 °, P) )(AB) = (XY)
B. (R y = x û r (90 °, P) )(AB) = (XY)
D. (T < 0, −1 > û r (90 °, P) )(AB) = (XY)
15
Name: ________________________
____ 48. In the diagram, ABC ≅
ABC onto LMN ?
ID: A
LMN . What is a congruence transformation that maps
A. (R y = −x )( ABC) = (
LMN)
B. (r (90 °, O ) û R y = −x )( ABC) = ( LMN)
C. (R y = x û T < 0, −2 > )( ABC) = ( LMN)
D. (R y = −x û T < 0,2 > )( ABC) = ( LMN)
____ 49. Which figures are congruent?
A. B ≅ D and A ≅ C
B. B ≅ D
C. B ≅ D and E ≅ F
D. B ≅ D and E ≅ F and A ≅ C
16
Name: ________________________
ID: A
____ 50. The dashed-lined figure is a dilation image of EFGH. Is D (n , H ) an enlargement or a reduction? What is the
scale factor n of the dilation?
A. n = 6; enlargement
C. n = 3; reduction
1
D. n = ; reduction
3
B. n = 3; enlargement
____ 51. The dashed-lined figure is a dilation image of
ABC with center of dilation P (not shown). Is D (n , P ) an
enlargement, or a reduction? What is the scale factor n of the dilation?
A. reduction;
n=2
B. reduction;
1
n=
4
C. enlargement;
n=2
D.
reduction;
1
n=
2
____ 52. A blueprint for a house has a scale factor n = 45. A wall in the blueprint is 9 in. What is the length of the
actual wall?
A. 4,860 feet
B. 33.75 in.
C. 405 feet
D. 33.75 feet
17
Name: ________________________
ID: A
____ 53. A microscope shows you an image of an object that is 140 times the object’s actual size. So the scale factor
of the enlargement is 140. An insect has a body length of 6 millimeters. What is the body length of the insect
under the microscope?
A. 840 centimeters
C. 84 millimeters
B. 8,400 millimeters
D. 840 millimeters
____ 54. The zoom feature on a camera lens allows you dilate what appears on the display. When you change from
100% to 500%, the new image on your screen is an enlargement of the previous image with a scale factor of
5. If the new image is 47.5 millimeters wide, what was the width of the previous image?
A. 9.5 millimeters
C. 118.75 millimeters
B. 23.75 millimeters
D. 237.5 millimeters
55. The endpoints of AB are A(9, 4) and B(5, –4). The endpoints of its image after a dilation are A′(6, 3) and
B ′(3, − 3).
a. Explain how to find the scale factor.
b. Locate the center of dilation. Show your work.
56. What are the vertices of ∆ABC for D 2 ( ABC) ? Graph D 2 ( ABC) .
18
Name: ________________________
ID: A
57. What are the images of the vertices of ∆ABC when you apply the composition D(0.5, O) û Rx = 4 ? Graph
(D(0.5, O ) û Rx = 4 )( ABC).
58. ∆ABC has vertices A(0,0), B(5,−1) , and C(3,7). What are the vertices of the resulting image when the
triangle is translated 4 units to the left then dilated by a scale factor of 2?
____ 59. What composition of rigid motions and a dilation maps EFGH to the dashed figure?
A. D (3,(2, −2)) û T < 4, −1 >
C. D (3,(2, −2)) û T < −4,1 >
B. D ( 1 ,(2, −2)) û T < 4, −1 >
D. D ( 1 ,(2, −2)) û T < −4,1 >
3
3
60. You have a 5” by 7” photo that you would like to have enlarged to fit an 8” by 10” frame. Would the two
photographs be similar? Explain.
19
ID: A
Unit 5 - Test Study Guide
Answer Section
1. ANS:
NAT:
STA:
KEY:
2. ANS:
NAT:
STA:
KEY:
3. ANS:
NAT:
STA:
KEY:
4. ANS:
NAT:
STA:
KEY:
5. ANS:
NAT:
STA:
KEY:
6. ANS:
NAT:
STA:
KEY:
7. ANS:
NAT:
STA:
KEY:
8. ANS:
NAT:
STA:
KEY:
9. ANS:
NAT:
STA:
KEY:
10. ANS:
NAT:
STA:
KEY:
11. ANS:
NAT:
STA:
KEY:
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 1 Identifying an Isometry
transformation | rigid motion
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 2 Naming Images and Corresponding Parts
image | preimage | rigid motion
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 2 Naming Images and Corresponding Parts
image | preimage | corresponding parts | rigid motion
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
translation | transformation | image | preimage
A
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
translation | transformation | preimage | image
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
translation | preimage | image
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation | preimage | image
B
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation | image | preimage
A
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation
C
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
translation | word problem
1
ID: A
12. ANS: C
PTS: 1
DIF: L3
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
KEY: translation
13. ANS: D
PTS: 1
DIF: L3
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
KEY: translation
14. ANS: D
PTS: 1
DIF: L3
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation
KEY: translation
15. ANS: B
PTS: 1
DIF: L4
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 5 Composing Translations
KEY: translation
16. ANS:
a. AB ≅ MN , BC ≅ NJ , CD ≅ JK , DE ≅ KL, EA ≅ LM
b. J
PTS: 1
DIF: L4
NAT: CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-1 Problem 2 Naming Images and Corresponding Parts
KEY: transformation | image | preimage | multi-part question | rigid motion
17. ANS:
T < 2,2 > (A) = (−6 + 2, 2 + 2) → A′(−4, 4)
T < 2,2 > (B) = (−2 + 2, 4 + 2) → B ′(0, 6)
T < 2,2 > (C) = (−4 + 2, − 4 + 2) → C ′(−2, − 2)
PTS:
NAT:
STA:
KEY:
1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 3 Finding the Image of a Translation
transformation | image | preimage | translation
2
ID: A
18. ANS:
a.
b. The school is 10 blocks north and 2 block west of Megan’s house.
School = T < −2,10 > (Megan’s house)
19.
20.
21.
22.
23.
24.
PTS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
ANS:
NAT:
STA:
KEY:
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-1 Problem 5 Composing Translations
problem solving | multi-part question | transformation | translation | word problem
B
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
D
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
C
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 1 Reflecting a Point Across a Line
reflection | line of reflection
3
ID: A
25. ANS:
NAT:
STA:
KEY:
26. ANS:
NAT:
STA:
KEY:
27. ANS:
NAT:
STA:
KEY:
28. ANS:
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | line of reflection
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 3 Writing a Reflection Rule
reflection | line of reflection
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 3 Writing a Reflection Rule
reflection | line of reflection
PTS:
NAT:
STA:
KEY:
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | image | preimage | line of reflection
4
ID: A
29. ANS:
PTS:
NAT:
STA:
KEY:
30. ANS:
[4]
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | image | preimage | line of reflection
a. Answers may vary. Sample: (0, –2) and (2, 0)
b. The line that contains the two points is the perpendicular bisector of AA′ and BB ′ .
c.
[3]
[2]
[1]
error in calculation of one coordinate of the two points on the line of reflection
only two parts correct
only one part correct
PTS:
NAT:
STA:
KEY:
1
DIF: L4
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-2 Problem 2 Graphing a Reflection Image
reflection | reflection line | extended response | rubric-based question
5
ID: A
31. ANS:
NAT:
STA:
KEY:
32. ANS:
NAT:
STA:
KEY:
33. ANS:
NAT:
STA:
KEY:
34. ANS:
a–b.
C
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | center of rotation | angle of rotation
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | center of rotation | angle of rotation
B
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | center of rotation | angle of rotation
Vertices: W ′(5,3), X ′(3,1), Y ′(5,−1), Z ′(7,1)
PTS:
NAT:
STA:
KEY:
35. ANS:
NAT:
TOP:
36. ANS:
NAT:
TOP:
1
DIF: L3
CC G.CO.2| CC G.CO.4| CC G.CO.5| CC G.CO.6| G.2.b| G.2.c| G.2.d
NC 3.01
TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane
rotation | angle of rotation | center of rotation
B
PTS: 1
DIF: L2
CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
9-4 Problem 2 Reflections Across Intersecting Lines
KEY: isometry
A
PTS: 1
DIF: L4
CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
9-4 Problem 3 Finding a Glide Reflection Image
KEY: glide reflection | isometry
6
ID: A
37. ANS:
PTS: 1
STA: NC 3.01
KEY: isometry
38. ANS:
DIF: L3
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines
PTS: 1
STA: NC 3.01
KEY: isometry
DIF: L4
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines
7
ID: A
39. ANS:
PTS:
STA:
KEY:
40. ANS:
[4]
1
NC 3.01
isometry
DIF: L3
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
TOP: 9-4 Problem 2 Reflections Across Intersecting Lines
a-b.
c. r (180 °, O ) (AB), a rotation of 180° about the origin
[3]
[2]
[1]
description of isometry missing
correct coordinates named without graphs
only two parts correct
PTS: 1
DIF: L4
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
TOP: 9-4 Problem 3 Finding a Glide Reflection Image
KEY: isometry | glide reflection | extended response | rubric-based question | rigid motion
8
ID: A
41. ANS:
Yes. The reflection lines do not intersect because the three points lie on the same line. Because the line of
reflection is the perpendicular bisector of the segment connecting a point and its image, both lines of
reflection are perpendicular to the line that passes through all three points. Since both lines of reflection are
perpendicular to the same line, they are parallel.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
PTS:
STA:
KEY:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
ANS:
NAT:
TOP:
KEY:
ANS:
NAT:
TOP:
KEY:
ANS:
STA:
KEY:
ANS:
STA:
KEY:
ANS:
STA:
KEY:
ANS:
STA:
KEY:
1
DIF: L4
NAT: CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
NC 3.01
TOP: 9-4 Problem 1 Reflections Across Parallel Lines
isometry | writing in math | reasoning
D
PTS: 1
DIF: L3
CC G.CO.2| CC G.CO.5| CC G.CO.6| G.2.d| G.2.g
STA: NC 3.01
9-4 Problem 3 Finding a Glide Reflection Image
KEY: isometry | glide reflection
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 1 Identifying Equal Measures
D
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 1 Identifying Equal Measures
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 1 Identifying Equal Measures
A
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 2 Identifying Congruent Figures
KEY: congruent | rigid motion
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 2 Identifying Congruent Figures
KEY: congruent | rigid motion
D
PTS: 1
DIF: L4
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 3 Identifying Congruence Transformations
congruent | congruence transformation
C
PTS: 1
DIF: L2
CC G.CO.6| CC G.CO.7| CC G.CO.8
STA: NC 3.01
9-5 Problem 5 Determining Congruence
congruent | congruence transformation
B
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 1 Finding a Scale Factor
dilation | enlargement | scale factor
D
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 1 Finding a Scale Factor
dilation | reduction | scale factor
D
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length
dilation | enlargement | scale factor | word problem
D
PTS: 1
DIF: L3
NAT: CC G.CO.2| G.2.c| G.2.d
NC 3.01
TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length
dilation | enlargement | scale factor | word problem
9
ID: A
54. ANS: A
PTS: 1
DIF: L4
NAT: CC G.CO.2| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length
KEY: dilation | enlargement | scale factor | word problem
55. ANS:
a. Find the length of each segment. Then divide the length of the image by the length of the preimage.
AB =
A′B ′ =
(9 − 5) 2 + (4 − (−4)) 2 = 4 5
(6 − 3) 2 + (3 − (−3)) 2 = 3 5
The scale factor is
3 5
4 5
3
, or .
4
b.
The center is (–3, 0).
PTS: 1
DIF: L4
NAT: CC G.CO.2| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-6 Problem 1 Finding a Scale Factor
KEY: multi-part question | dilation | reduction | center of dilation | scale factor | coordinate plane | graphing
10
ID: A
56. ANS:
D 2 (A) = ((2) ⋅ (−2),(2) ⋅ (4)), or A′(−4,8)
D 2 (B) = ((2) ⋅ (4),(2) ⋅ (2)), or B ′(8,4)
D 2 (C) = ((2) ⋅ (−4),(2) ⋅ (−4)), or C ′(−8,−8)
PTS: 1
DIF: L4
NAT: CC G.CO.2| G.2.c| G.2.d
STA: NC 3.01
TOP: 9-6 Problem 2 Finding a Dilation Image
KEY: dilation | reduction | center of dilation | scale factor | coordinate plane | graphing
57. ANS:
A″ = (5,2)
B ″ = (2,1)
C ″ = (6,−2)
PTS: 1
STA: NC 3.01
DIF: L3
NAT: CC G.SRT.2| CC G.SRT.3
TOP: 9-7 Problem 1 Drawing Transformations
11
ID: A
58. ANS:
T < −4,0 > (A) = (0 − 4,0) = A′(−4,0)
T < −4,0 > (B) = (5 − 4,−1) = B ′(1,−1)
T < −4,0 > (C) = (3 − 4,7) = C ′(−1,7)
D 2 (A′) = (2 ⋅ (−4),2 ⋅ 0) = A″(−8,0)
D 2 (B ′) = (2 ⋅ 1,2 ⋅ (−1)) = B ″(2,−2)
D 2 (C ′) = (2 ⋅ (−1),2 ⋅ 7) = C ″(−2,14)
PTS: 1
DIF: L3
NAT: CC G.SRT.2| CC G.SRT.3
STA: NC 3.01
TOP: 9-7 Problem 1 Drawing Transformations
59. ANS: A
PTS: 1
DIF: L4
NAT: CC G.SRT.2| CC G.SRT.3
STA: NC 3.01
TOP: 9-7 Problem 2 Describing Transformations
KEY: similar | similarity transformation | rigid motion
60. ANS:
No, the two photographs would not be similar. In order for them to be similar, all measurements would have
to be multiplied by the same scale factor.
PTS: 1
DIF: L2
NAT: CC G.SRT.2| CC G.SRT.3
STA: NC 3.01
TOP: 9-7 Problem 4 Determining Similarity
KEY: similarity | similarity transformation
12