538 CHAPTER 8 Geometry a) If the trough is filled with water, determine the number of cubic feet of water contained in the trough. 67.88 ft3 ≈ b) Determine the total weight, assuming that the trough weighs 375 lb and the water weighs 62.4 lb per cubic foot. Is the base strong enough to support the trough filled with water? 4610.71 lb; ≈ yes c) If 1 gal of water weighs 8.3 lb, how many gallons of water will the trough hold? 510.33 gal ≈ 8.5 In Exercises 32 and 33, use the given triangle and reflection lines to construct the indicated reflections. Show the triangle in the positions both before and after the reflection. m B A C l 32. Construct the reflection of triangle ABC about line l. * 33. Construct the reflection of triangle ABC about line m * In Exercises 34 and 35, use translation vectors v and w to construct the indicated translations. Show the rectangle in the positions both before and after the translation. A C w v D B 34. Construct the translation of rectangle ABCD using translation vector v. * 35. Construct the translation of rectangle ABCD using translation vector w. * In Exercises 36–38, use the given figure and rotation point P to construct the indicated rotations. Show the trapezoid in the positions both before and after the rotation. A D C B P 36. Construct a 90° rotation of parallelogram ABCD about point P. * 37. Construct a 180° rotation of parallelogram ABCD about point P. * 38. Construct a 270° rotation of parallelogram ABCD about point P. * In Exercises 39 and 40, use the given figure, translation vectors v and w, and reflection lines l and m to construct the indicated glide reflections. Show the triangle in the positions both before and after the glide reflection. m v l w C A B 39. Construct a glide reflection of triangle ABC using vector v and reflection line l. * 40. Construct a glide reflection of triangle ABC using vector w and reflection line m. * In Exercises 41 and 42, use the following figure to answer the following questions. C B A m l 41. Does triangle ABC have reflective symmetry about line l? Explain. Yes 42. Does triangle ABC have reflective symmetry about line m? Explain. No *See Instructor Answer Appendix
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