Coordinate Geometry A figure that has a vertex at (3, 4) has the given line of symmetry. Tell the coordinates of another vertex of the figure.

41. the y-axis
42. the x-axis
43. the line y = x y equals x

C Challenge

Coordinate Geometry Graph each equation and describe its symmetry.

44. y = x 2 y equals , x squared
45. y = ( x + 2 ) 2 y equals . open x plus . 2 , close squared
46. y = x 3 y equals , x cubed
47. y = | x | y equals vertical line x vertical line
48. x 2 + y 2 = 9 x squared , plus , y squared , equals 9

For each three-dimensional figure, draw a net that has point symmetry and a net that has 1, 2, or 4 lines of symmetry.

49. 
50. 

    Square pyramid

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

51. What is the smallest angle, in degrees, through which you can rotate a regular hexagon onto itself?

52. You place a sprinkler so that it is equidistant from three rose bushes at points A, B, and C. How many feet is the sprinkler from A?

    

53. Δ S T U cap delta s t u  has vertices S ( 1 , 2 ) , T ( 0 , 5 ) , and  U ( − 8 , 0 ) . s open 1 comma 2 close comma t open 0 comma 5 close comma , and u open negative 8 comma 0 close .  What is the x-coordinate of S after a 270 ° 270 degrees  rotation about the origin?
54. The diagonals of rectangle PQRS intersect at O. P O = 2 x − 5 p o equals . 2 x minus 5  and O R = 7 − x . o r equals . 7 minus x .  What is the length of Q S ¯ ? q s bar , question mark
55. The length of the hypotenuse of a 45 ° - 45 ° - 90 ° 45 degrees , minus , 45 degrees , minus , 90 degrees  triangle is 55 in. What is the length of one of its legs to the nearest tenth of an inch?

Mixed Review

See Lesson 9-3.

56. Which capital letters of the alphabet are rotation images of themselves? Draw each letter and give an angle of rotation ( < 360 ° ) . open less than . 360 degrees close .

See Lesson 6-7.

57. Three vertices of an isosceles trapezoid are ( − 2 , 1 ) , ( 1 , 4 ) , and  ( 4 , 4 ) . open negative 2 comma 1 close comma open 1 comma 4 close comma , and , open 4 comma 4 close .  Find all possible coordinates for the fourth vertex.

Get Ready! To prepare for Lessons 9-5, do Exercises 58–60.

See Lesson 7-2.

Determine the scale drawing dimensions of each room using a scale of 1 4 in . = 1 ft . 1 fourth , in . , equals 1 , ft .

58. kitchen: 12 ft by 16 ft
59. bedroom: 8 ft by 10 ft
60. laundry room: 6 ft by 9 ft

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