43. Use the diagram below. Find the coordinates of the given point.

    

    1. A ′ , eh prime comma  the reflection image of A across y = x y equals x
    2. A ″ , eh double prime comma  the reflection image of A ′ eh prime  across y = − x y equals , negative x
    3. A ‴ , eh triple prime comma  the reflection image of A ″ eh double prime  across y = x y equals x
    4. A ″ ″ , eh double prime double prime comma  the reflection image of A ‴ eh triple prime  across y = − x y equals , negative x
    5. How are A and A ″ ″ eh double prime double prime  related?

C Challenge

Reasoning Can you form the given type of quadrilateral by drawing a triangle and then reflecting one or more times? Explain.

44. parallelogram
45. isosceles trapezoid
46. kite
47. rhombus
48. rectangle
49. square
50. Coordinate Geometry Show that B(b, a) is the reflection image of A(a, b) across the line y = x . y equals x .  (Hint: Show that y = x y equals x  is the perpendicular bisector of A B ¯ . eh b bar , . )

Standardized Test Prep

SAT/ACT

51. What is the reflection image of (a, b) across the line y = − 6 ? y equals . negative 6 question mark
    1. ( a − 6 , b ) open eh minus 6 comma b close
    2. ( a , b − 6 ) open eh comma b minus 6 close
    3. ( − 12 − a , b ) open minus . 12 minus eh comma b close
    4. ( a , − 12 − b ) open eh comma minus . 12 minus b close
52. The diagonals of a quadrilateral are perpendicular and bisect each other. What is the most precise name for the quadrilateral?
    6. rectangle
    7. parallelogram
    8. rhombus
    9. kite
53. A D → eh d vector  bisects ∠ A angle eh  of Δ C A B , cap delta c eh b comma  with point D on C B ¯ . c b bar , .  Which of the following is true?
    1. C D D B = C A B A fraction c d , over d b end fraction . equals . fraction c eh , over b eh end fraction
    2. C D D B = B A C A fraction c d , over d b end fraction . equals . fraction b eh , over c eh end fraction
    3. C B C D = C A B A fraction c b , over c d end fraction . equals . fraction c eh , over b eh end fraction
    4. C A C B = A B D B fraction c eh , over c b end fraction . equals . fraction eh b , over d b end fraction

Extended Response

54. Write an indirect proof of the following statement: The hypotenuse of a right triangle is the longest side of the right triangle.

Mixed Review

For the given points, A ′ B ′ ¯ eh prime , b prime bar  is a translation of A B ¯ . eh b bar , .  Write a rule to describe each translation.

See Lesson 9-1.

55. A ( − 1 , 5 ) , B ( 2 , 0 ) , A ′ ( 3 , 3 ) , B ′ ( 6 , − 2 ) eh open negative 1 comma 5 close comma b open 2 comma 0 close comma , eh prime , open 3 comma 3 close comma , b prime , open 6 comma negative 2 close
56. A ( − 9 , − 4 ) , B ( − 7 , 1 ) , A ′ ( − 4 , − 3 ) , B ′ ( − 2 , 2 ) eh open negative 9 comma negative 4 close comma b open negative 7 comma 1 close comma , eh prime , open negative 4 comma negative 3 close comma , b prime , open negative 2 comma 2 close

See Lesson 7-2.

57. Maps A map of Alberta, Canada, uses the scale 1  cm = 25  km . 1 cm equals 25 , km .  On the map, the distance from Calgary to Edmonton is 11.1 cm. How far apart are the two cities?

Get Ready! To prepare for Lesson 9-3, do Exercises 58–63.

See p. 824.

Use a protractor to draw an angle with the given measure.

58. 120 ° 120 degrees
59. 90 ° 90 degrees
60. 72 ° 72 degrees
61. 60 ° 60 degrees
62. 45 ° 45 degrees
63. 36 ° 36 degrees

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