20. Travel Your friend and her parents are visiting colleges. They leave their home in Enid, Oklahoma, and drive to Tulsa, which is 107 mi east and 18 mi south of Enid. From Tulsa, they go to Norman, 83 mi west and 63 mi south of Tulsa. Where is Norman in relation to Enid?

B Apply

21. In the diagram below, the orange figure is a translation image of the red figure. Write a rule that describes the translation.

    
    Image Long Description

22. Think About a Plan Δ M U G cap delta m u g  has coordinates M ( 2 , − 4 ) , U ( 6 , 6 ) , and  G ( 7 , 2 ) . m open 2 comma negative 4 close comma u open 6 comma 6 close comma , and g open 7 comma 2 close .  A translation maps point M to M ′ ( − 3 , 6 ) . m prime , open negative 3 comma 6 close .  What are the coordinates of U ′ u prime  and G ′ g prime  for this translation?
    • How can you use a graph to help you visualize the problem?
    • How can you find a rule that describes the translation?
23. Coordinate Geometry PLAT has vertices P ( − 2 , 0 ) , L ( − 1 , 1 ) , A ( 0 , 1 ) , p open negative 2 comma 0 close comma l open negative 1 comma 1 close comma eh open 0 comma 1 close comma  and T ( − 1 , 0 ) . P ′ L ′ A ′ T ′ t open negative 1 comma 0 close . . p prime , l prime , eh prime , t prime  is the image of PLAT for the translation ( x , y ) → ( x + 2 , y − 3 ) . open x comma y close rightwards arrow . open x plus 2 comma y minus 3 close .  Show that P P ′ ¯ , L L ′ ¯ , A A ′ ¯ , p , p prime bar . comma . l , l prime bar . comma . eh , eh prime bar . comma  and T T ′ ¯ t , t prime bar  are all parallel.

Geometry in 3 Dimensions Follow the sample below. Use each figure, graph paper, and the given translation to draw a three-dimensional figure.

SAMPLE Use the rectangle and ( x , y ) → ( x + 3 , y + 1 ) open x comma y close rightwards arrow . open x plus 3 comma y plus 1 close  to draw a box.

• Step 1

  

• Step 2

  

24. ( x , y ) → ( x + 2 , y − 1 ) open x comma y close rightwards arrow . open x plus 2 comma y minus 1 close

    

25. ( x , y ) → ( x − 2 , y + 2 ) open x comma y close rightwards arrow . open x minus 2 comma y plus 2 close

    

26. ( x , y ) → ( x − 3 , y − 5 ) open x comma y close rightwards arrow . open x minus 3 comma y minus 5 close

    

27. Open-Ended You are a graphic designer for a company that manufactures wrapping paper. Make a design for wrapping paper that involves translations.
28. Reasoning The translation ( x , y ) → ( x + 5 , y + 7 ) open x comma y close rightwards arrow . open x plus 5 comma y plus 7 close  maps Δ M N O cap delta m n o  onto Δ M ′ N ′ O ′ . cap delta , m prime , n prime , o prime , .  What translation rule maps Δ M ′ N ′ O ′ . cap delta , m prime , n prime , o prime , .  onto Δ M N O ? cap delta m n o question mark

29. Landscaping The diagram below shows the site plan for a backyard storage shed. Local law, however, requires the shed to sit at least 15 ft from property lines. Describe how to move the shed to comply with the law.

    

30. Computer Animation You write a computer animation program to help young children learn the alphabet. The program draws a letter, erases the letter, and makes it reappear in a new location two times. The program uses the following composition of translations to move the letter.

    ( x , y ) → ( x + 5 , y + 7 ) open x comma y close rightwards arrow . open x plus 5 comma y plus 7 close  followed by ( x , y ) → ( x − 9 , y − 2 ) open x comma y close rightwards arrow . open x minus 9 comma y minus 2 close

    Suppose the program makes the letter W by connecting the points (1, 2), (2, 0), (3, 2), (4, 0) and (5, 2). What points does the program connect to make the last W?

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