25. Recreation When you play pool, you can use the fact that the ball bounces off the side of the pool table at the same angle at which it hits the side. Suppose you want to put the ball at point B into the pocket at point P by bouncing it off side R S ¯ . r s bar , .  Off what point on R S ¯ r s bar  should the ball bounce? Draw a diagram and explain your reasoning.

    

26. Think About a Plan The coordinates of the vertices of Δ F G H cap delta f g h  are F ( 2 , − 1 ) , G ( − 2 , − 2 ) , and  H ( − 4 , 3 ) . f open 2 comma negative 1 close comma g open negative 2 comma negative 2 close comma , and h open negative 4 comma 3 close .  Graph Δ F G H cap delta f g h  and its image Δ F ′ G ′ H ′ cap delta , f prime , g prime , h prime  for a reflection across the line y = x − 3 . y equals . x minus 3 .
    • What is the relationship between the line y = x − 3 y equals . x minus 3  and F F ′ ¯ , G G ′ ¯ , f , f prime bar . comma . g , g prime bar . comma  and H H ′ ¯ ? h , h prime bar . question mark
    • How can you use slope to find the image of each vertex?

Copy each pair of figures. Then draw the line of reflection you can use to map one figure onto the other.

27. 
28. 
29. 

30. History The work of artist and scientist Leonardo da Vinci (1452–1519) has an unusual characteristic. His handwriting is a mirror image of normal handwriting.

    

    1. Write the mirror image of the sentence, “Leonardo da Vinci was left-handed.” Use a mirror to check how well you did.
    2. Explain why the fact about da Vinci in part (a) might have made mirror writing seem natural to him.
31. Open-Ended Give three examples from everyday life of objects that come in a left-handed version and a right-handed version.

Find the image of O(0, 0) after two reflections, first across line ℓ 1 bold italic script l sub 1  and then across line ℓ 2 . bold italic script l sub 2 , .

32. ℓ 1 : y = 3 , ℓ 2 : x - axis script l sub 1 , colon y equals 3 comma , script l sub 2 , colon x minus , axis
33. ℓ 1 : x = − 2 , ℓ 2 : y - axis script l sub 1 , colon x equals . negative 2 comma , script l sub 2 , colon y minus , axis
34. ℓ 1 : x - axis , ℓ 2 : y - axis script l sub 1 , colon x minus , axis , comma , script l sub 2 , colon y minus , axis
35. ℓ 1 : x = − 2 , ℓ 2 : y = 3 script l sub 1 , colon x equals . negative 2 comma , script l sub 2 , colon y equals 3
36. ℓ 1 : y = 3 , ℓ 2 : x = − 2 script l sub 1 , colon y equals 3 comma , script l sub 2 , colon x equals . negative 2
37. ℓ 1 : x = − 2 , ℓ 2 : y = x script l sub 1 , colon x equals . negative 2 comma , script l sub 2 , colon y equals x
38. ℓ 1 : x = a , ℓ 2 : y = b script l sub 1 , colon x equals eh comma , script l sub 2 , colon y equals b
39. ℓ 1 : x = a , ℓ 2 : y = x script l sub 1 , colon x equals eh comma , script l sub 2 , colon y equals x
40. ℓ 1 : y = b , ℓ 2 : y = x script l sub 1 , colon y equals b comma , script l sub 2 , colon y equals x

41. Reasoning When you reflect a figure across a line, does every point on the preimage move the same distance? Explain.

42. Security Recall that when a ray of light hits a mirror, it bounces off the mirror at the same angle at which it hits the mirror. You are installing a security camera. At what point on the mirrored wall should you aim the camera at C in order to view the door at D? Draw a diagram and explain your reasoning.

    

    Mirrored wall

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