Geometry A Chapter 4 Test Review Answer Key

Review Chapter 4 Geometry A Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. D D B C D C D D D A D A D D SHORT ANSWER 15. C' (6, 3), D' (8, 13), E' (8, 6) 16. BÕ = (0,-1) CÕ = (2,-3) DÕ = (5,-2) 17. S ʹ(−2, −3), T ʹ(−1, 0) S ʺ (3, −2), T ʺ (0, −1) 18. A ʹ(−2, 2), B ʹ(0, −2), C ʹ(4, 0), D ʹ(2, 3) 19. RSF is a 90¡ rotation about the origin of AXN. VHQ is a reflection of ICG in the y-axis. 20. PROBLEM 21. 4 Lines of Symmetry 4 Rotation Symmetry 22. one horizontal line of symmetry 23. 1 Line of Symmetry 0 Rotation Symmetry 24. dilation scale factor: 2 25. ( x, y) → ( x − 2, y + 8) OTHER 26. a. (x, y) → (x + 6, y − 4) b. about 7.21 m i c. about 27.04 m i/h Full marks are not necessarily awarded for a correct answer with no work. Answers must be supported by work and or explanations. In particular, solutions found from a graphic display should be supported by sketching these parts. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written work. Therefore you are advised to show all work. Review Chapter 4 Geometry A Multiple Choice ____ 1. (4.1A) In the diagram, name the vector and select its component form. ⎯⎯ → A. BC , −5, 3 B. CB , −3, 5 ⎯⎯ → ____ 2. (4.1B) Write a rule for the translation of ⎯⎯ → C. CB , 5, −3 ⎯⎯ → D. BC , 3, −5 ABC to A ʹB ʹC ʹ. (Hint: Scale is by 2Õs) A. B. ____ C. ( x, y) → ( x − 2, y + 2) ( x, y) → ( x − 2, y + 2) D. ( x, y) → ( x + 2, y − 2) ( x, y) → ( x − 1, y − 2) 3. (4.1C) An architect is designing a garden for a client on a planning sheet. The client requests the relocation of a water fountain by the rule (x, y) → (x + 2, y − 4). Later, the client decides that they would prefer the water fountainÕs location moved from this new position 5 units to the right and 4 units up. Find the composition as a single transformation. A. B. ( x, y) → ( x + 7, y − 8) ( x, y) → ( x + 7, y + 0) C. ( x, y) → ( x − 3, y + 8) D. ( x, y) → ( x − 7, y − 0) ____ 4. (4.1C) Segment CD has endpoints C (Ð 7, 4) and D (Ð 8, 6) Find CÕÕ and DÕÕafter the composition. Translation: (x, y) → (x + 1, y − 4) Translation: (x, y) → (x + 2, y + 2) A. ____ CÕÕ(-10, 2) C. CÕÕ(-4, 2) DÕÕ(-11, 4) DÕÕ(-5, 4) B. CÕÕ(-4, 6) D. CÕÕ(-9, 7) DÕÕ(-5, 8) DÕÕ(-10, 9) 5. (4.2A) The vertices of DEF are D (Ð 4, Ð4), E (Ð 2, Ð3), and F (Ð2, 0). Graph D ʹE ʹF ʹ after the reflection over the line y = −x. A. C. B. D. DEF and its image ____ ____ 6. (4.2B) Graph ABC with vertices A (Ð5, 1), B (Ð1, 4) and C (0, 0) and its image glide reflection. Translation: (x, y) → (x + 1, y) Reflection: x-axis A. C. B. D. A ʺ B ʺ C ʺ after the 7. (4.3A) Which graph shows the polygon and its image after a rotation of 90¡ about the origin? A. C. B. D. ____ 8. (4.3A) Which graph shows the polygon and its image after a rotation of 180¡ about the origin? A. C. B. ____ D. 9. (4.3B) Graph ST with endpoints at S(−2, −1) and T(2, 3) and its image S ʺ T ʺ after the composition. Translation: ( x, y) → ( x − 3, y + 2) ; Rotation: 270 degrees about the origin A. SÕÕ = (1,5) C. TÕÕ = (5,-1) B. SÕÕ = (-1,5) D. TÕÕ = (-5,-1) ____ 10. (4.5C) Find the scale factor of the dilation. Then enlargement. A. B. 4 ; reduction 9 5 ; enlargement 4 C. D. SÕÕ = (1,-5) TÕÕ = (-5,-1) SÕÕ = (1,5) TÕÕ = (5,1) tell whether the dilation is a reduction or an 9 ; enlargement 4 4 ; reduction 5 ____ 11. (4.5C) Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 3 5 ; reduction C. ; enlargement 5 3 3 8 B. D. ; reduction ; enlargement 8 3 ____ 12. (4.5B) An image of a celebrity is going to be used on a promotional billboard. The person is 6.5 feet tall in real life, and 16.25 feet tall on the billboard. What is the scale factor of this dilation? A. A. 2.5 feet C. 0.4 feet B. 11.375 feet D. 9.75 feet ____ 13. (4.5A) A copy machine is set to enlarge an image 259%. If the original image is 5 inches tall, how tall will the enlarged image be? A. about 1295 in. C. about 7.59 in. B. about 264 in. D. about 12.95 in. ____ 14. (4.5A) You want to enlarge a picture by a factor of 3 from its current size of 3 inches by 5 inches. What is the size of the enlarged picture? A. B. 6 in. by 15 in. 9 in. by 8 in. C. 6 in. by 8 in. D. 9 in. by 15 in. Short Answer 15. (4.1A) The vertices of CDE are C (3, Ð3), D (5, 7), and E (5, 0). Translate and write the coordinates for CDE using vector 3, 6 . C ʹD ʹE ʹ C ʹ__________ D ʹ__________ E ʹ__________ 16. (4.2A) BCD has vertices B (0, 1), C (2, 3) and D (5, 2) and its image after the reflection over the x − axis. Write the coordinates of B ʹC ʹD ʹ B ʹ__________ C ʹ__________ D ʹ__________ 17. (4.3B) ST with endpoints at S(2, −1) and T(3, 2) and its images after the compositions. Translation ( x, y) → ( x − 4, y − 2) Rotation: 90 degrees about the origin a. Find S ʹT ʹ S ʹ__________ T ʹ__________ b. Find S ʺ T ʺ S ʺ __________ T ʺ __________ 18. (4.5A) Quadrilateral ABCD with vertices A(−5, 5), B(0, −5), C(10, 0) and D(5, 7.5) and its image after a dilation centered at (0, 0) with a scale factor of 0.4. Write the coordinates for A ʹB ʹC ʹD ʹ A ʹ__________ B ʹ__________ C ʹ__________ D ʹ__________ 19. (4.1D) Identify the transformations. A. ANX is a pre-image and B . ICG is a pre-image and SRF is an image. _______________________ HVQ is an image.______________________ 20. (4.2A) Graph BCD with vertices B (2, 1), C (3, 3) and D (3, 1) and its image reflection over the line x = 1. B ʹC ʹD ʹ after the Problem (4.2C) (4.3C) #21 Draw in the lines of reflection symmetry. Then find how many rotations of symmetry it has. 21. ________________________ 22. (4.2C) Draw in a line reflection symmetry (if any) of the word CHECKBOOK (4.2C) (4.3C) #23 Draw in the lines of reflection symmetry. Then find how many rotations of symmetry it has. 23. ________________________ (4.5A) Describe the transformation that maps the preimage to the image. 24. ________________________ (4.1B) #25, Write a rule, in translation notation, for the translation of the preimage to the image. 25. ______________________________________ Other 26. (4.1D) A car begins at point A. During its trip, the car moves in a straight line until it reaches a point B that is 2 miles south and 3 miles east relative to point A. The car then immediately moves to its final destination (point C) which is 2 miles south and 3 miles east relative to point B. The entire trip takes 16 minutes. a. Write the transformation as a single composition in translation notation. ___________________________________ b. Let the carÕs final destination be point C. What is the straight line distance from the carÕs starting point to point C? Work: _________________________ c. Find the carÕs average speed throughout the entire trip in miles per hour. _________________________