Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
Choose the term that best completes each sentence.
Review for Ch 9 Geo Test (Not Worth pts) 1. When a transformation is applied to a figure, and then another transformation is applied to its image this is a(n) (composition of transformations, order of symmetries).
2. If a figure is folded across a straight line and the halves match exactly, the fold line is called the (line
of reflection, line of symmetry).
3. A (dilation, glide reflection) enlarges or reduces a figure proportionally.
Choose the term that best completes each sentence.
Choose the term that best completes each sentence.
4. The number of times a figure maps onto itself as it rotates from 0¡ to 360¡ is called the (magnitude of symmetry, order of symmetry). 8. To rotate a point (90¡, 180¡) counterclockwise about the origin, multiply the y­coordinate by ­1 and then interchange the x­ and y­coordinates. 5. A (line of reflection, translation vector) is the same distance from each point of a figure and its image. 9. A (vector, reflection) is a congruence transformation.
6. A figure has (a center of rotation, symmetry) if it can be mapped onto itself by a rigid motion. 7. A glide reflection includes both a reflection and a (rotation, translation). 10. A figure has (plane symmetry, rotational symmetry) if the figure can be mapped onto itself by a rotation
between from 0¡ and 360¡ about the center of the figure. 1
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
Graph each figure and its image under the given reflection.
Graph each figure and its image under the given reflection.
11. Rectangle ABCD with A(2, –4), B(4, –6), C(7, –3), and D(5, –1) in the x­axis 12. Triangle XYZ with X(–1, 1), Y(–1, –2), and Z(3, –3) in the y­axis Graph each figure and its image under the given reflection.
13. Graph ÆABC with vertices A(0, –1), B(2, 0), C(3, –3) and its image along 14. Label the preimage ABCD and then graph and label the image accurately using the translation
2
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
Graph each figure and its image after the specified rotation about the origin.
16. ÆDGF with vertices D(1, 2), G(2, 3), F(1, 3); 90¡ Graph each figure and its image after the specified rotation about the origin.
15. ÆMNO with vertices M(–2, 2), N(0, –2), O(1, 0); 180¡ Draw ALL lines of symmetry or write NONE.
17.
19.
Decide if the figure has plane symmetry, axis symmetry, both or neither. 18.
21.
20.
22.
3
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
State whether each figure has rotational symmetry. Write yes or no. If yes, state the order and magnitude of symmetry.
October 31, 2016
25a) What kind of transformation creates èA’B’C’ from the preimage of èABC?
b) If the center is at (0, 0), what is the scale factor?
23.
24.
y
B'
A'
B
A
x
C
C'
26. Determine whether the dilation from figure W to W’ is an enlargement or a reduction. Then find the scale factor of the dilation AND x.
27. The members of the Math Club use an overhead projector to make a poster. If the original image was 6 inches wide and the image of the poster is 4 feet wide, what is the scale factor of the enlargement?
4
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
28. Point N has coordinates (4, –3). What will the coordinate of the image be after a reflection across the y­axis?
29. What is the angle of rotation that maps T onto T’ in the figure below? 31. Given a Ç b and is cut by transversal t, which statement below justifies the conclusion that Ú1¤Ú2?
30. Which of the following is a side length in isosceles triangle DEF? a) alternate exterior angles are congruent
a) 2 cm b) 8 cm
c) 9 cm d) 11 cm
b) alternate interior angles are congruent
c) corresponding angles are congruent
d) vertical angles are congruent
5
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
32. Does the figure have rotational symmetry. If yes, state the order and magnitude of symmetry. 33. Regina left her office downtown and traveled 3 blocks west and 5 blocks north. Write a translation vector to describe her route.
35. What vector best describes the translation in the figure below?
34. Dilate the figure shown on the coordinate grid by a scale factor of 1.5 centered at the origin.
y
A
A'
E
D
F
x
6
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
37. A picture that is 5 in by 8 inches is to be enlarged 3.5 times to make a poster. What are the dimensions of the poster?
36. Name all the rigid motions and explain why they are rigid motions.
38. EXPLAIN how you would reflect an image over the y­axis. 39. Name the image of S under reflection in line n? n
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Review for Ch 9 Geo Test answers to graphs at bottom.notebook
October 31, 2016
Answers:
40. If figure F were reflected in line u and then line v describe a single transformation that maps F into F″. Include the size (magnitude) of the transformation.
a)
u
F
1. Composition of transformations 2. Line of symmetry 3. Dilation 4. Order of symmetry 5. Line of reflection 6. Symmetry 7. Translation 8. 90¡ 9. Reflection 10. Rotational symmetry 19. None 20. Both 21. Both 22. Both 23. Yes, order = 4, mag = 90¡ 24. No 25a) dilation b) 3 27. 8 28. N’(–4, –3) 29. 135¡ 30. D 31. C 32. Yes, order = 4, mag = 90¡ 98¡
36. Reflection, translation, rotation, glide reflection because the sides and angles of the image and preimage are congruent. 37. 17 in by 28 in 38. Change the sign of the x value or on a graph count the number of spaces to the y­axis and then go that many more past it. 39. T 40a) rotation, 196¡ 40b) translation, 6 in (answers to graphs on website)
v
Kind of transformation: ________________
size (magnitude) : ________________
Answers cont.
Answers cont.
11.
12.
B'
15.
A'
C'
X
X'
D'
D
M
Y
Y'
N
B
13.
14.
B'
A
D
B
A
D
D'
M'
B
A'
C'
F'
G
O'
Z
Z'
F
G'
N'
O
C
A
16.
18.
17.
C
B'
A'
1
C
D'
6
C'
8
Review for Ch 9 Geo Test answers to graphs at bottom.notebook
40. If figure F were reflected in line u and then line v describe a single transformation that maps F into F″. Include the size (magnitude) of the transformation.
Answers cont.
y
34.
October 31, 2016
E'
b)
F
E
u
3 in
F'
D'
v
D
F
x
Kind of transformation: ________________
size (magnitude) : ________________
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