31. Use the graph below. Write three different translation rules for which the image of Δ J K L cap delta j k l  has a vertex at the origin.

    

Find a translation that has the same effect as each composition of translations.

32. ( x , y ) → ( x + 2 , y + 5 ) open x comma y close rightwards arrow . open x plus 2 comma y plus 5 close  followed by ( x , y ) → ( x − 4 , y + 9 ) open x comma y close rightwards arrow . open x minus 4 comma y plus 9 close
33. ( x , y ) → ( x + 12 , y + 0.5 ) open x comma y close rightwards arrow . open x plus 12 comma y plus 0.5 close  followed by ( x , y ) → ( x + 1 , y − 3 ) open x comma y close rightwards arrow . open x plus 1 comma y minus 3 close

C Challenge

34. Coordinate Geometry Δ A B C cap delta eh b c  has vertices A ( − 2 , 5 ) , B ( − 4 , − 1 ) , eh open negative 2 comma 5 close comma b open negative 4 comma negative 1 close comma  and C ( 2 , − 3 ) . c open 2 comma negative 3 close .  Show that the images of the midpoints of the sides of Δ A B C cap delta eh b c  are the midpoints of the sides of Δ A ′ B ′ C ′ cap delta , eh prime , b prime , c prime  for the translation ( x , y ) → ( x + 4 , y + 2 ) . open x comma y close rightwards arrow . open x plus 4 comma y plus 2 close .
35. Writing Explain how to use translations to draw a parallelogram.

Standardized Test Prep

SAT/ACT

36. Δ A B C cap delta eh b c  has vertices A ( − 5 , 2 ) , B ( 0 , − 4 ) , and  C ( 3 , 3 ) . eh open negative 5 comma 2 close comma b open 0 comma negative 4 close comma , and c open 3 comma 3 close .  What are the vertices of the image of Δ A B C cap delta eh b c  under the translation ( x , y ) → ( x + 7 , y − 5 ) ? open x comma y close rightwards arrow . open x plus 7 comma y minus 5 close question mark
    1. A ′ ( 2 , − 3 ) , B ′ ( 7 , − 9 ) , C ′ ( 10 , − 2 ) eh prime , open 2 comma negative 3 close comma , b prime , open 7 comma negative 9 close comma , c prime , open 10 comma negative 2 close
    2. A ′ ( − 12 , − 3 ) , B ′ ( − 7 , − 9 ) , C ′ ( − 4 , − 2 ) eh prime , open negative 12 comma negative 3 close comma , b prime , open negative 7 comma negative 9 close comma , c prime , open negative 4 comma negative 2 close
    3. A ′ ( − 12 , 7 ) , B ′ ( − 7 , 1 ) , C ′ ( − 4 , 8 ) eh prime , open negative 12 comma 7 close comma , b prime , open negative 7 comma 1 close comma , c prime , open negative 4 comma 8 close
    4. A ′ ( 2 , − 3 ) , B ′ ( 10 , − 2 ) , C ′ ( 7 , − 9 ) eh prime , open 2 comma negative 3 close comma , b prime , open 10 comma negative 2 close comma , c prime , open 7 comma negative 9 close

37. What is the value of x in the figure below?

    

    6. 4.5
    7. 16
    8. 18
    9. 18.5
38. In Δ P Q R , P Q = 4.5 , Q R = 4.4 , and  R P = 4.6 . cap delta p q r comma p q equals 4.5 comma q r equals 4.4 comma , and r p equals 4.6 .  Which statement is true?
    1. m ∠ P + m ∠ Q < m ∠ R m angle p plus m angle q less than m angle r
    2. ∠ Q  is the largest angle . angle q . isthelargestangle . .
    3. ∠ R  is the largest angle . angle r . isthelargestangle . .
    4. m ∠ R < m ∠ P m angle r less than m angle p

Short Response

39. ▱ white parallelogram ABCD has vertices A ( 0 , − 3 ) , B ( − 4 , − 2 ) , and  D ( − 1 , 1 ) . eh open 0 comma negative 3 close comma b open negative 4 comma negative 2 close comma , and d open negative 1 comma 1 close .
    1. What are the coordinates of C?
    2. Is ▱ white parallelogram ABCD a rhombus? Explain.

Mixed Review

See Lesson 8-5.

40. Navigation An airplane lands at a point 100 km east and 420 km south from where it took off. Describe the magnitude and the direction of its flight vector.

See Lesson 4-7.

41. Given: B C ¯ ≅ E F ¯ , B C ¯ ‖ E F ¯ , A D ¯ ≅ D C ¯ ≅ C F ¯ table with 2 rows and 1 column , row1 column 1 , b c bar , approximately equal to , e f bar , comma , b c bar . double vertical bar . e f bar , comma , row2 column 1 , eh d bar , approximately equal to , d c bar , approximately equal to , c f bar , end table

    Prove: A B ¯ ≅ D E ¯ eh b bar , approximately equal to , d e bar

    

Get Ready! To prepare for Lesson 9-2, do Exercises 42-44.

See Lesson 3-8.

Write an equation for the line through A perpendicular to the given line.

42. A ( 1 , − 2 ) ; x = − 2 eh open 1 comma negative 2 close semicolon x equals negative 2
43. A ( − 1 , − 1 ) ; y = 1 eh open negative 1 comma negative 1 close semicolon y equals 1
44. A ( − 1 , 2 ) ; y = x eh open negative 1 comma 2 close semicolon y equals x

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