49. Multiplying Vectors Suppose you ride your bike 5 mi on a bike path. Your friend rides 10 mi on the same path in the same direction. If w ⇀ modified w with right harpoon up above represents your bike ride, then 2 w ⇀ 2 , modified w with right harpoon up above represents your friend's bike ride. This is an example of scalar multiplication of vectors. Suppose w ⇀ = 〈 2 , 4 〉 . modified w with right harpoon up above , equals . left pointing angle bracket 2 comma 4 right pointing angle bracket . .

    1. Describe 2 w ⇀ 2 , modified w with right harpoon up above as an ordered pair.
    2. Find the magnitudes of w ⇀ modified w with right harpoon up above and 2 w ⇀ . 2 , modified w with right harpoon up above , . What is their relationship?
    3. Based on your results for parts (a) and (b), what is the effect of multiplying a vector by a constant? Explain.

C Challenge

50. Geometry in 3 Dimensions A hot-air balloon traveled 2000 ft north and 900 ft east, while rising 400 ft. This trip can be described with the three-coordinate vector 〈 2000 , 900 , 400 〉 . left pointing angle bracket , 2000 , comma 900 comma 400 right pointing angle bracket . What is the magnitude of the vector? What is the angle of elevation of the balloon from its starting point?
51. Writing Think of the number zero and its properties. Define a zero vector and justify your definition.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

52. A boat heads due east directly across a river at 30 ft/min. The river flows south at 20 ft/min. To the nearest ft/min, what is the resultant speed of the boat?

    

53. The lengths of the legs of a right triangle are 6 and 11. To the nearest hundredth, what is the length of the hypotenuse?
54. The medians A E ¯ , B F ¯ , eh e bar , comma , b f bar , comma and C D ¯ c d bar of Δ A B C cap delta eh b c intersect at G. If G D = 4 , g d , equals 4 comma what is CD?
55. The circumference of a circle is 24 mm. To the nearest tenth of a mm, what is the radius of the circle? Use 3.14 for π . pi .

Mixed Review

See Lesson 8-4.

56. Indirect Measurement A hot-air balloon pilot sights the landing field from a height of 2000 ft. The angle of depression is 24 ° . 24 degrees . To the nearest foot, what is the ground distance from the hot-air balloon to the landing field?

See Lesson 6-7.

57. Is the quadrilateral with vertices A ( − 1 , − 5 ) , B ( 6 , − 5 ) , C ( 9 , 3 ) , eh open negative 1 comma , negative 5 , close comma b open 6 comma , negative 5 , close comma c open 9 comma 3 close comma and D ( 2 , 3 ) d open 2 comma 3 close a parallelogram? Explain.

See Lesson 4-1.

Get Ready! To prepare for Lesson 9-1, do Exercises 58–63.

Δ A B C ≅ Δ E F G . cap delta eh b c approximately equal to , cap delta e f g , . Complete the congruence statements.

58. A B ¯ ≅ ? _ eh b bar , approximately equal to , modified question mark with under bar below
59. E G ¯ ≅ ? _ e g bar , approximately equal to , modified question mark with under bar below
60. F G ¯ ≅ ? _ f g bar , approximately equal to , modified question mark with under bar below
61. ∠ C ≅ ? _ angle c , approximately equal to , modified question mark with under bar below
62. ∠ E ≅ ? _ angle e approximately equal to , modified question mark with under bar below
63. ∠ B ≅ ? _ angle b approximately equal to , modified question mark with under bar below

Table of Contents