55. Shadows A flashlight projects an image of rectangle ABCD on a wall so that each vertex of ABCD is 3 ft away from the corresponding vertex of A ′ B ′ C ′ D ′ . eh prime , b prime , c prime , d prime , .  The length of A B ¯ eh b bar  is 3 in. The length of A ′ B ′ ¯ eh prime , b prime bar  is 1 ft. How far from each vertex of ABCD is the light?

    

Standardized Test Prep

SAT/ACT

56. A dilation maps Δ C D E cap delta c d e  onto Δ C ′ D ′ E ′ . cap delta , c prime , d prime , e prime , .  If C D = 7.5  ft , C E = 15  ft , D ′ E ′ = 3.25  ft , and  C ′ D ′ = 2.5  ft , c d equals 7.5 , ft comma c e equals 15 , ft comma , d prime , e prime , equals , 3.25 , ft comma , and , c prime , d prime , equals 2.5 , ft comma  what is DE?
    1. 1.08 ft
    2. 5 ft
    3. 9.75 ft
    4. 19 ft
57. You want to prove indirectly that the diagonals of a rectangle are congruent. As the first step of your proof, what should you assume?
    6. A quadrilateral is not a rectangle.
    7. The diagonals of a rectangle are not congruent.
    8. A quadrilateral has no diagonals.
    9. The diagonals of a rectangle are congruent.
58. Which word can describe a kite?
    1. equilateral
    2. equiangular
    3. convex
    4. scalene

Short Response

59. Use the figure below to answer the questions below.

    

    1. Does the figure have rotational symmetry? If so, identify the angle of rotation.
    2. Does the figure have reflectional symmetry? If so, how many lines of symmetry does it have?

Mixed Review

Coordinate Geometry A figure with a vertex at ( − 2 , 7 ) open negative 2 comma 7 close  has the given type of symmetry. State the coordinates of another vertex of the figure.

See Lesson 9-4.

60. point symmetry centered at the origin
61. line symmetry across the y-axis

Get Ready! To prepare for Lesson 9-6, do Exercises 62–64.

Given points R ( − 1 , 1 ) , S ( − 4 , 3 ) , and  T ( − 2 , 5 ) , r open negative 1 comma 1 close comma s open negative 4 comma 3 close comma , and t open negative 2 comma 5 close comma  graph Δ R S T cap delta r s t  and its reflection image across each line.

See Lesson 9-2.

62. the y-axis
63. the x-axis
64. y = 1 y equals 1

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