1. What term describes a transformation that does not change a figure s size or shape?

Transcription

1 1. What term describes a transformation that does not change a figure s size or shape? () similarity () isometry () collinearity (D) symmetry For questions 2 4, use the diagram showing parallelogram D. E H I F D G 2. reflection across EG carries parallelogram D onto itself. () True () False 3. rotation of 90 about I carries parallelogram D onto itself. () True () False 4. rotation of 180 about I carries parallelogram D onto itself. () True () False 5. Which of these is equivalent to a translation? () a reflection across one line () a composition of two reflections across intersecting lines () a composition of two reflections across parallel lines Page 1 of 47 Revised 11/13/2012 lark ounty School District

2 6. regular polygon with n sides is carried onto itself by a positive rotation about its center that is a multiple of 60, but less than 360. Which could NOT be the value of n? () 3 () 4 () 5 (D) 6 7. In the diagram, g h and lies on line g. 10 cm 5 cm g The figure is reflected across line g, and its image is reflected across line h. What is the distance from line g to the final image of point? () 5 cm () 15 cm () 20 cm (D) 25 cm 8. What is the image of the point ( 4, 6) under the transformation T x, y y, x () (6, 4) () ( 6, 4) () (4, 6) (D) ( 4, 6) h? Page 2 of 47 Revised 11/13/2012 lark ounty School District

3 9. figure is rotated about the origin by 180, then is translated 4 units right and one unit up. Which describes the results of the two transformations? () x, y x 4, y 1 () x, y x 4, y 1 () x, y y 4, x 1 (D) x, y y 4, x The point (4, 3) is rotated 90 about the origin. In which quadrant is '? () I () II () III (D) IV 11. figure is reflected across the line y = 2, then reflected across the line y = 4. Which single transformation results in the same image? () a reflection across the line y = 3 () a reflection across the line y = 6 () a translation 2 units up (D) a translation 4 units up 12. Point is the image of point under a transformation T. Line is the perpendicular bisector of at point M. Which describes the transformation T? () a reflection across () a 90 rotation about M () a translation by the vector from to M (D) a dilation about M with scale factor Page 3 of 47 Revised 11/13/2012 lark ounty School District

4 For questions 13 16, determine if the described transformation(s) is/are an isometry. 13. reflection is an isometry. () True () False 14. composition of two reflections is an isometry. () True () False 15. dilation is an isometry. () True () False 16. composition of a rotation and a dilation is an isometry. () True () False 17. In, M is the midpoint of and N is the midpoint of. For which type of triangle is 1 MN? 2 () equilateral only () isosceles only () scalene only (D) any triangle Page 4 of 47 Revised 11/13/2012 lark ounty School District

5 18. Use the diagram. m k Which series of reflections would result in a rotation of 44 about? () reflect across k then reflect across () reflect across then reflect across k () reflect across then reflect across m (D) reflect across m then reflect across 19. fter a figure is rotated, P P. Which statement(s) could be true? () The center of rotation is P. () The angle of rotation is a multiple of 360. () Either or or both. (D) Neither nor Page 5 of 47 Revised 11/13/2012 lark ounty School District

6 For questions 20 23, use the diagram where is the reflection of across PQ. P Q 20. P = P () True () False 21. PQ () True () False 22. Q = Q () True () False 23. PQ 1 2 () True () False Page 6 of 47 Revised 11/13/2012 lark ounty School District

7 For questions 24 26, use the diagram where D is a quadrilateral with D and D. Diagonals and D intersect at E. E D 24. E E () True () False 25. DE E () True () False 26. DE E () True () False Page 7 of 47 Revised 11/13/2012 lark ounty School District

8 27. Use the figure. transformation T is defined as x, y x, y. Which shows the image of figure under T? () () () Page 8 of 47 Revised 11/13/2012 lark ounty School District

9 For questions 28 29, a transformation S is defined as x, y 3 x, y The pre-image of 3, 6 under S is 9, 5 () True () False 29. S is an isometry. () True () False Given point is located at (1, 3). What is the final image of after this series of transformations? (1) Reflect across the y axis. (2) Translate the image such that x, y x 4, y 2. () ( 1, 3) () ( 3, 5) () ( 3, 1) (D) ( 5, 5) 31. Which transformation does NOT preserve the orientation of a figure? () dilation () reflection () rotation (D) translation Page 9 of 47 Revised 11/13/2012 lark ounty School District

10 For questions 32 35, determine if the mapping is an isometry. 32. x, y x, y 2 () True () False 33. x, y x, y () True () False 34. x, y y, x () True () False 35. x, y 2 x, y () True () False is an isometry. is an isometry. is an isometry. is an isometry. 36. figure is transformed in the plane such that no point maps to itself. What type of transformation must this be? () dilation () reflection () rotation (D) translation Page 10 of 47 Revised 11/13/2012 lark ounty School District

11 For questions 37 38, determine the truth of the statements about rotations. 37. Rotations preserve the orientation of a figure. () True () False 38. Under a rotation, no point can map to itself. () True () False For questions 39 41, point P is located at (6, 0) and undergoes a transformation. 39. rotation of 90 about P results in P = P. () True () False 40. translation by the vector 6, 0 results in P = P. () True () False 41. reflection about the x axis results in P = P. () True () False Page 11 of 47 Revised 11/13/2012 lark ounty School District

12 For questions 42 43, use the diagram which shows has been reflected across an unknown line, then reflected across line m to produce. y m x 42. The equation of line is x = 0.5. () True () False 43. If were reflected across line m first, then reflected across line to produce, the equation of line would be x = 0.5. () True () False Page 12 of 47 Revised 11/13/2012 lark ounty School District

13 For questions 44 46, consider a triangle that has been transformed through rigid motions and its image compared to XYZ. Determine if the given information is sufficient to draw the provided conclusion. 44. Given onclusion X Y XYZ Z () True () False 45. Given onclusion X Y XYZ YZ () True () False 46. Given onclusion X XY XYZ YZ () True () False Page 13 of 47 Revised 11/13/2012 lark ounty School District

14 47. Look at the figure below. Look at these three figures. II I III Which figures are congruent to the first figure? () I only () II only () I and II only (D) I, II, and III 48. Use the diagram. 1 r s m n Which statement would be used to prove lines r and s are parallel? () 1 and 3 are congruent () 2 and 7 are complementary () 4 and 1 are congruent (D) 8 and 6 are supplementary Page 14 of 47 Revised 11/13/2012 lark ounty School District

15 For questions 49 51, evaluate whether the image of a figure under the described transformation is congruent to the figure. 49. transformation T follows the rule x, y x 3, y congruent to the figure. () True () False 50. transformation T follows the rule x, y y, x congruent to the figure. () True () False 51. transformation T follows the rule x, y x, 2y to the figure. () True () False. The image of a figure under T is. The image of a figure under T is. The image of a figure under T is congruent 52. In the diagram, m n and p q. p q m n x 88 What is the value of x? () 44 () 88 () 92 (D) Page 15 of 47 Revised 11/13/2012 lark ounty School District

16 For questions 53 54, consider 53. m m 140 () True () False 54. m 100 () True () False where = and m Use the Venn diagram. Quadrilaterals I II Parallelograms Rhombi Squares Rectangles III IV V Trapezoids VI VII Kites quadrilateral D has 4 lines of symmetry. Identify the area of the diagram in which D resides. () III () IV () V (D) VII Page 16 of 47 Revised 11/13/2012 lark ounty School District

17 56. On the coordinate plane, draw triangles and such that: (1) = (2) has been rotated In the diagram, m is the perpendicular bisector of at, and rm D E. D m E Prove D E. 58. In the diagram, D is the perpendicular bisector of. D Prove D D. 59. Prove the sum of the measures of the interior angles of any triangle is Page 17 of 47 Revised 11/13/2012 lark ounty School District

18 60. onstruct an equilateral triangle inscribed in circle O. O 61. Use the figure. y F D E x (a) Transform by reflecting it across the y-axis to produce. (b) Describe a transformation, or composition of transformations, that maps (c) Describe a single transformation that maps to DEF. to DEF Page 18 of 47 Revised 11/13/2012 lark ounty School District

19 62. Jimmy is building a go-cart to race. Jimmy sits in a seat toward the left rear corner of the cart. To see other carts behind him, he mounts 3 plane mirrors: one on each side of the cart and one in the center. The scale diagram shows a top view of the cart. Front of art center mirror left side mirror right side mirror J Seat 1 foot (a) Jimmy s eyes are at point J. The mirrors are mounted in a way that Jimmy does not block his own view. Show the area behind the cart that Jimmy can see using the mirrors. (b) Describe how Jimmy could improve his visibility behind the cart using the same three mirrors Page 19 of 47 Revised 11/13/2012 lark ounty School District

20 63. The diagram shows regular hexagon DEF with center O. F O E D For each part, fill in the blank. (a) is the image of under a 60 rotation about O. (b) The figure is reflected across D. The pre-image of E is. (c) F is the image of D when the figure is rotated about O. (d) is first reflected across F. That image maps to F when reflected across. 64. Draw the image of when reflected across line m. m Page 20 of 47 Revised 11/13/2012 lark ounty School District

21 65. Draw the image of when rotated 70 about O. O Page 21 of 47 Revised 11/13/2012 lark ounty School District

22 66. is the image of when a reflected about line. onstruct line. ' ' ' Page 22 of 47 Revised 11/13/2012 lark ounty School District

23 67. is the image of when rotated about point O. onstruct point O and compute the angle of rotation. ' ' ' Page 23 of 47 Revised 11/13/2012 lark ounty School District

24 68. Use scalene right triangle. Describe and sketch the transformations required so that the union of the triangle and its image forms (a) a kite. (b) an isosceles triangle. (c) a rectangle Page 24 of 47 Revised 11/13/2012 lark ounty School District

25 69. Right triangle PQR has sides of length 6 units, 8 units, and 10 units. The triangle is dilated by a scale factor of 4 about point Q. What is the area of triangle P'Q'R'? () 96 square units () 192 square units () 384 square units (D) 768 square units 70. In the diagram below DH. D 4 9 H 8 y What is the value of y? () 13 () 18 () The ratio of the side lengths of a triangle is 3:6:8. second triangle is similar to the first and its shortest side measures 8.0 centimeters. What is the length of the longest side of the second triangle? () 3.0 cm () 10.7 cm () 13.0 cm (D) 21.3 cm Page 25 of 47 Revised 11/13/2012 lark ounty School District

26 72. In the diagram, a student has placed a mirror on level ground, then stands so that the top of a nearby tree is visible in the mirror. 2 m 3 m 36 m What is the height of the tree? () 24 m () 35 m () 41 m (D) 59 m 73. In the diagram, JG QR. Q J 7 R x 4 G 8 P What is the value of x? () 11 () 6 () 5 (D) Page 26 of 47 Revised 11/13/2012 lark ounty School District

27 74. Which figure contains two similar triangles that are NOT congruent? () () () (D) 75. Sally constructs a triangle where two of the angles measure 50 and 60. Tom constructs a triangle where two of the angles measure 50 and 70. What is true about the two triangles? () The triangles cannot be similar. () The triangles could be similar. () The triangles must be similar. 76. Triangle has vertices 2, 2, 5, 5, and 5, 3 point 1, 1 with scale factor 4. What is the location of '? () 8, 8 () 10, 10 () 11, 5 (D) 14, 6. The triangle is dilated about the Page 27 of 47 Revised 11/13/2012 lark ounty School District

28 77. Use the diagram. y m x Dilate line m about the origin with scale factor 2. What is the equation of the line s image? () y = 2x + 2 () y = 2x + 4 () y = 4x + 2 (D) y = 4x Which is NOT a criterion for triangle similarity? () angle-angle () angle-side-angle () side-angle-side (D) side-side Page 28 of 47 Revised 11/13/2012 lark ounty School District

29 79. Use the diagram. m y P x Dilate line m by a factor 1 2 about P. Which shows the result of the dilation? () y m' () y m' P x P x () m' y (D) y m' P x P x Page 29 of 47 Revised 11/13/2012 lark ounty School District

30 80. In the diagram, segments and D intersect at E, F lies on, and m E 60. D E F 60 The two segments are dilated about F with scale factor 1 2. What is m E? () 30 () 60 () 90 (D) Page 30 of 47 Revised 11/13/2012 lark ounty School District

31 For questions 81 83, use the diagram. E F D G F Let the figure be dilated with scale factor k, where k 0 and k m E k m E. () True () False 82. G' is between ' and F'. () True () False 83. D k D () True () False Page 31 of 47 Revised 11/13/2012 lark ounty School District

32 84. In the diagram, D is dilated with center O to produce '''D', and 1. 3 O D' ' ' F ' D What is O? () 1 3 () 1 2 () 2 (D) Page 32 of 47 Revised 11/13/2012 lark ounty School District

33 85. Use the figure below. Which shows the figure dilated about the origin with scale factor 1.5? () () () 86. One vertex of a polygon is ( 4, 5). If the polygon is dilated about the point (0, 2) with scale factor 2, what is the location of? () ( 8, 8) () ( 8, 10) () (8, 10) (D) (8, 4) Page 33 of 47 Revised 11/13/2012 lark ounty School District

34 87. J (5, 7) is the image of J(3, 3) after a dilation with scale factor 3. Where is the center of dilation? () ( 3, 9) () (0, 0) () (2, 1) (D) (4, 5) 88. Fred stands at corner of a rectangular field shown below. He needs to get to corner. 9 m D 12 m What is the shortest distance from to? () 9 m () 13 m () 15 m (D) 21 m 89. Use the right triangle. What is the value of x? x 15 8 What is the value of x? () 7 () 161 () 7 (D) Page 34 of 47 Revised 11/13/2012 lark ounty School District

35 90. Use the diagram. b h a x D y c Which is equal to h? () () () (D) ay bx xy ab 91. Use the diagram. E F D Given: D E Prove: E D Page 35 of 47 Revised 11/13/2012 lark ounty School District

36 92. In the diagram, is a dilation of. ' ' ' (a) Find the center of dilation O. (b) ompute the scale factor of the dilation. 93. Prove that any two isosceles right triangles are similar. 94. In the diagram, is a right triangle with right angle, and D is an altitude of. b a d e D c Use the fact that D D to prove a b c. 95. Triangle One has vertices (2, 4), (2, 8), and (5, 4). Triangle Two is similar to Triangle One and has two of its vertices at ( 1, 1) and ( 7, 1). (a) Draw Triangle One and Triangle Two on the coordinate plane and label the vertices. (b) Draw and label a third triangle that is similar to Triangle One, has two vertices at ( 1, 1) and ( 7, 1), but is not congruent to Triangle Two Page 36 of 47 Revised 11/13/2012 lark ounty School District

37 96. (HONORS) Triangle has sides of length 3, 6, and 8. Triangle DEF is similar to triangle and has one side with length 24. (a) What are the possible scale factors of the dilation of triangle to triangle DEF? (b) ompute one possible area of triangle DEF. 97. (HONORS) The diagram shows a surveyor s map. 950 m m The surveyor is trying to measure the direct distance between points and, which are on opposite sides of a lake. From point, point is 950 meters away in a direction 20 west of north. From point, point is 880 meters away in a direction 50 east of north. Which represents the distance between and? 2 2 () cos70 () () sin50 sin sin70 sin (HONORS) onsider a triangle. Which statement is true? () () () (D) c a b 2abcos c a b 2abcos c a b 2abcos c a b 2abcos Page 37 of 47 Revised 11/13/2012 lark ounty School District

38 99. (HONORS) small airplane flies due north at 150 kilometers per hour. wind is blowing towards the direction 60 east of north at 50 kilometers per hour. Which figure represents the final speed and direction of the airplane? N N N () () () (D) N 100. (HONORS) Use the diagram. 4 7 What is cos? () () () (D) Page 38 of 47 Revised 11/13/2012 lark ounty School District

39 For questions , consider a triangle and each given set of measurements (HONORS),, and m are sufficient to solve the triangle using the Law of Sines. () True () False 102. (HONORS),, and m are sufficient to solve the triangle using the Law of Sines. () True () False 103. (HONORS),, and are sufficient to solve the triangle using the Law of Sines. () True () False 104. (HONORS) The diagram shows a parallelogram D D What is the parallelogram s area? () () 15 () 15 3 (D) Page 39 of 47 Revised 11/13/2012 lark ounty School District

40 105. (HONORS) In the diagram, is a non-right triangle. a b c Which describes the area of the triangle? () 1 2 ab () absin () 1 sin 2 ab (D) 1 cos 2 ab 106. (HONORS) Given: cos and sin What is the approximate value of cos 154? () 0.90 () 0.44 () 0.44 (D) Page 40 of 47 Revised 11/13/2012 lark ounty School District

41 For questions use the statement below. Given: n angle measures k, where k > sin k cos 90 k () True () False 108. (HONORS) sin k sin 180 k () True () False 109. (HONORS) cos k cos 180 k () True () False 110. Let cos m. What is the value of sin? () m () 1 m () 2 1 m (D) 1 m Page 41 of 47 Revised 11/13/2012 lark ounty School District

42 111. In where is a right angle, 7 sin. What is cos? 4 () () () 3 4 (D) Use the diagram Which statement is true? () () () 13 sin 5 12 cos tan Page 42 of 47 Revised 11/13/2012 lark ounty School District

43 113. Use the diagram x Which is the value of x? () () () (D) x 41cos35 x tan x cos35 41 x tan Use the diagram. 5 2 d 45 What is the value of d? () 5 () 5 2 () 10 (D) Page 43 of 47 Revised 11/13/2012 lark ounty School District

44 For questions , let cos x m (HONORS) cos 180 x () True () False 116. cos 90 x () True () False 117. sin 90 x () True () False = m = m = m 118. Let a cos28. Which statement is true? () a cos 62 () a cos 152 () a sin 62 (D) a sin What is cos 1 3 2? () 30 () 45 () 60 (D) Page 44 of 47 Revised 11/13/2012 lark ounty School District

45 120. In the diagram, < D and D = D. D Which statement is true? () cos sin D () cos sin D () cos sin D 121. What is tan 60? () () () (D) What is tan 1 () 30 () 45 () 60 (D) 90? Page 45 of 47 Revised 11/13/2012 lark ounty School District

46 123. In GHI, the sine of angle G equals 1 2. GHI is a dilation of GHI about G with a scale factor of 2. What is the sine of angle G'? () 1 4 () 1 2 () (D) (HONORS) In triangle, m 25, a = 6.2, and b = 4. Find all possible measures of the remaining two angles and the third side (HONORS) In triangle, m 25, a = 6.2, and c = 4. (a) Find all possible measures of the remaining two angles and the third side. (b) Find all possible areas of the triangle Page 46 of 47 Revised 11/13/2012 lark ounty School District

47 126. The diagram shows a model of a closet floor on which Kim is laying carpet. (Measurements are approximate.) (a) What is the area of the closet? (b) The carpet Kim is using is cut by the carpet store in rectangular pieces from a 4-foot wide roll. What is the shortest length of carpet Kim would need to cover the closet floor in a single piece? Justify your answer Page 47 of 47 Revised 11/13/2012 lark ounty School District