PARCC Assessment Readiness UNIT 5 Review/Test Organizer Objective: Provide review and practice for this chapter and standardized tests. Standard Items MCC9-12.G.CO.1 1 MCC9-12.G.CO.2 2, 4–7, 13, 16, 21, 31, 39 MCC9-12.G.CO.3 10–12, 25–28 MCC9-12.G.CO.4 3, 37 MCC9-12.G.CO.5 8, 9, 14, 15, 17, 18–20, 22–24, 29, 30, 32–36, 38, 39 Resources Assessment Resources Unit Assessment Go to my.hrw.com for updated online PARCC-aligned Assessment Readiness. PARCC Assessment Readiness UNIT 5 REVIEW/TEST Selected Response 1. The change in position from the solid figure to the dashed figure is best described as a . -10 -8 10 2 4 6 8 x y 10 0 -10 -6 -6 -2 transmission translation rotation reflection 2. The image of point A under a 90° rotation about the origin is A�(10, -4). What are the coordinates of point A? (-10, -4) (-10, 4) (-4, -10) (4, 10) 3. Which are the angle of rotation and the order of rotational symmetry for the figure? 90°; 2 180°; 2 90°; 4 180°; 4 Use the graph for items 4–6. y - 2 2 2 2 4 4 - 4 4 - - - 4 4 - - - 2 2 2 2 4 4 A A B C D P Q R x 0 A 4. What are the coordinates of the image of point C under the same translation that maps point D to point B? (4, 4) (0, 4) (0, 8) (4, -8) 5. �PQR is rotated 180˚ about the origin. Which point is the image of point Q? A C B D 6. For which of the following combinations of transformations of �PQR would point A NOT be the image of point P? Reflection across the x-axis, followed by a horizontal translation of 4 units Reflection across the y-axis, followed by a horizontal translation of 4 units 180° rotation followed by a horizontal translation of -4 units Reflection across the line x = -2 followed by a vertical translation of 8 units 7. Which mapping represents three successive rotations of 90° about the origin? ( x, y ) → ( -x, -y ) ( x, y ) → ( x, -y ) ( x, y ) → ( -y, -x ) ( x, y ) → ( y, -x ) 500 Unit 5 Review/Test 500 Unit 5 Review/Test
Transcript
PARCC Assessment ReadinessUNIT 5 Review/Test
OrganizerObjective: Provide review and practice for this chapter and standardized tests.
Selected Response 1. The change in position from the solid figure to
the dashed figure is best described as a .
-10-8
10
2468
x
y
100-10 -6 -6-2
transmission
translation
rotation
reflection
2. The image of point A under a 90° rotation about the origin is A� (10, -4) . What are the coordinates of point A?
(-10, -4) (-10, 4) (-4, -10) (4, 10)
3. Which are the angle of rotation and the order of rotational symmetry for the figure?
90°; 2
180°; 2
90°; 4
180°; 4
Use the graph for items 4–6.
y
-222 222 444-444
---44
---22
22
44 AAB
C
DP
Q
R x
0
A
4. What are the coordinates of the image of point C under the same translation that maps point D to point B?
(4, 4) (0, 4) (0, 8) (4, -8)
5. �PQR is rotated 180˚ about the origin. Which point is the image of point Q?
A C
B D
6. For which of the following combinations of transformations of �PQR would point A NOT be the image of point P?
Reflection across the x-axis, followed by a horizontal translation of 4 units
Reflection across the y-axis, followed by a horizontal translation of 4 units
180° rotation followed by a horizontal translation of -4 units
Reflection across the line x = -2 followed by a vertical translation of 8 units
7. Which mapping represents three successive rotations of 90° about the origin?
(x, y) → (-x, -y)
(x, y) → (x, -y)
(x, y) → (-y, -x)
(x, y) → (y, -x)
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500 Unit 5 Review/Test
Mini-Task RubricItems 21–37
2 Points = The student’s answer is an accurate and complete execu-tion of the task or tasks.
1 Point = The student’s answer con-tains attributes of an appropriate response but is flawed.
0 Points = The student’s answer contains no attributes of an appro-priate response.
When problems involve geometric figures in the coordinate plane, it may be useful to describe properties of the figures algebraically. For example, you can use slope to verify that sides of a figure are parallel or perpendicular, or you can use the Distance Formula to find side lengths of the figure.
2
x
E′
F′
G′
y
0
-2-6
x
y
0
-2
-4
-6 -4 -2E′
F′
G′
10. What are the coordinates of the image of the point (5, 5) when it is reflected across the line y = 8?
(5, 13) (5, -3) (5, 11) (5, -5)
11. The point G (6, 7) is rotated 90° about point M (-9, -3) and then reflected across the line y = 9. What are the coordinates of the image G�?
(37, 6) (-24, 11) (-7, 12) (-19, 6)
12. How many lines of symmetry does a regular hexagon have?
1
3
6
12
13. What is the x-coordinate of the image of the point A (12, -7) after A is reflected across the x-axis?
-12
-7
7
12
8. Which regular polygon can be used with an equilateral triangle to tessellate a plane?
Heptagon
Octagon
Nonagon
Dodecagon
9. Which shows the image of �EFG after the translation (x, y) → (x – 6, y + 2) ?
xE
F
G
y
640
-2
-4
-6
2
4
x
y
0
-4
E′
F′
G′
2
6
x
y
40-4 -2
E′
F′G′
PARCC Assessment Readiness 501
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PARCC Assessment Readiness 501
Performance Task Rubric
Task Possible points
38a 3 points for correctly determining the new vertices of the bone fragment:
A (4, -1) C (8, -1) B (4, -3) D (8, -3)
b 3 points for correctly determining the new vertices of the bone fragment:
A (0, -1) C (4, -1) B (0, -3) D (4, -3)
Total possible points: 6
21. All of these properties are preserved except orientation because a reflection is an isometry.
22. rotation; DEFG → D′E′F′G′
23. translation; PQRS → P′Q′R′S′
24. X′ (-1, 1) ; Y′ (1, 4) ; Z′ (2, 3)
25. yes
26. yes
27. yes; 120°; 3
28. yes; 120°; 3
29.
14. Quadrilateral LMNO has vertices L(0, 4), M(3, 6), N(5, 4), and O(3, 0). If LMNO is reflected across the x-axis, which point(s) will not change location?
L and O
L
O
L and N
15. A triangle has vertices (0, 3), (0, 5), and (4, 5). The triangle is translated 2 units to the right and 2 units down. Which is one of the vertices of the translated triangle?
(2, 3)
(0, 1)
(4, 2)
(-2, 1)
16. Which of the following represents a reflection across the line y = 0?
(x, y) → (-x, y)
(x, y) → (x, -y)
(x, y) → (-x, -y)
(x, y) → (y, x)
17. What would be the coordinates of M(4, 3) after a rotation of 90° about the origin?
(0, 5)
(-2, 6)
(-3, 4)
(-1, 0)
18. A triangle has vertices A(1, 1), B(4, 1), and C(4, 3). After a transformation, the image has vertices A�(-1, 1), B�(-4, 1), and C�(-4, 3). Which of the following describes the transformation?
A rotation of 180° about the origin
A reflection across the x-axis
A reflection across the y-axis
A translation 2 units to the left
19. The vertices of triangle JKL are J(-3, -1), K(-1, -3), and L(-4, -4). Triangle JKL is reflected across the x-axis. What are the coordinates of K�?
(1, -3)
(-1, 3)
(-1, -3)
(1, 3)
20. Triangle PQR has vertices at P(2, 3), Q(3, 5), and R(5, 1). The triangle will be translated 4 units up. What will be the coordinates of point R�?
(2, 7)
(7, 5)
(9, 5)
(5, 5)
Mini-Tasks 21. �ABC is reflected across line m. What
observations can be made about �ABC and its reflected image �A�B�C� regarding the following properties: collinearity, betweenness, angle measure, triangle congruence, and orientation? Explain.
For items 22 and 23, identify the transformation. Then use arrow notation to describe the transformation.
22. E FD’ E’
G’ F’
D G
23. P Q
S R
P’ Q’
S’ R’
24. The coordinates for the vertices of �XYZ are X (-5, -4) , Y (-3, -1) , and Z (-2, -2) . Find the coordinates for the image of �XYZ after the translation (x, y) → (x + 4, y + 5) .
For items 25 and 26, tell whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry.
25.
26.
502 Unit 5 Review/Test
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502 Unit 5 Review/Test
31.
6-6
-6
6
0
y
xH′ J′
K′L′
H J
KL
33.4
0 4 -4
′
′ ′
34.4
-4
0 4 -4
′
′ ′
′
Performance Task Rubric
Task Possible points
39a 2 points for correctly determining the that the transformation is a translation. Each point in the preimage is slid 5 units to the right and 5 units down.
b 2 points for correctly determining the new coordinates of square ABCD:
A’ (2, -12) B’ (4, -10) C’ (6, -12) D’ (4, -14)
c 2 points for correctly determining that because translation preserves angle measure, the new image is also a right triangle
Total possible points: 6
30.
35. 4
-4
=
4 -4
′
′
′
36.
1
-4
-4
′
′
′ =
For items 27 and 28, tell whether the figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of symmetry.
27.
28.
For items 29 and 30, copy the given figure and use it to create a tessellation.
29.
30.
31. The coordinates of the vertices of rectangle HJKL are H(2, -1), J(5, -1), K(5, -3), and L(2, -3).
a. Graph HJKL in the coordinate plane.
b. Graph H�J�K�L� by applying the translation (x, y) → (x - 4, y + 1) to HJKL.
32. A triangle has vertices at (-1, 1), (1, 3), and (4, -2). After a reflection and a translation, the coordinates of the image are (5, 3), (3, 5), and (0, 0). Describe the reflection and the translation.
For items 33–36, reflect the figure with the given vertices across the given line.
33. E (-3, 2) , F (0, 2) , G (-2, 5) ; x-axis
34. J (2, -1) , K (4, -2) , L (4, -3) , M (2, -3) ; y-axis
35. P (2, -2) , Q (4, -2) , R (3, -4) ; y = x
36. A (2, 2) , B (-2, 2) , C (-1, 4) ; y = x
37. Many of the capital letters in our alphabet have horizontal or vertical lines of symmetry.
a. Make a list of the capital letters that have horizontal lines of symmetry.
b. Make a list of the capital letters that have vertical lines of symmetry.
c. Which capital letters have both horizontal and vertical lines of symmetry?
Performance Tasks 38. Archeologists examine digital images of their
excavations on a computer screen. They have the ability to move the image left, right, up, or down. They can also rotate the image. Suppose a computer screen has a coordinate grid transposed over it, and a bone fragment is in the shape of a rectangle that has the vertices A(4,-6) , B(4,-8) , C(8,-6) and D(8,-8) . Determine the effects that an archeologist’s actions will have on the bone fragment’s position on the screen.
a. First, the archeologist moves the bone fragment up 5 units on the screen. Find its new vertices.
b. Next, the archeologist moves the bone fragment left 4 units on the screen. What are its vertices now?
39. Square ABCD was transformed using the rule (x, y → x + 5, y - 5) to produce the image A�B�C�D�.
a. Is the transformation a reflection, a rotation, or a translation? How do you know?
b. The vertices of square ABCD are A(–3 –7) , B(–1, –5) , C(1, –7) , and D(–1, –9) . What are the coordinates of A�B�C�D�?
c. Right triangle QRS is transformed using the rule to produce the image Q�R�S�. Will �Q�R�S� be a right triangle? Explain.
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a. translation; each point in the preimage is slid 5 units to the right and 5 units down.
