9 Mid-Chapter Quiz

Do you know HOW?

Tell whether the transformation appears to be an isometry. Explain.

1. 
2. 
3. What rule describes the translation 5 units left and 10 units up?
4. Describe the translation ( x , y ) → ( x − 3 , y + 5 ) open x comma y close rightwards arrow . open x minus 3 , comma , y plus 5 close  in words.

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

   ( x , y ) → ( x + 7 , y − 2 ) open x comma y close rightwards arrow . open x plus 7 , comma , y minus 2 close  followed by ( x , y ) → ( x − 3 , y + 2 ) open x comma y close rightwards arrow . open x minus 3 , comma , y plus 2 close

Find the reflection image of ( 5 , − 3 ) open 5 comma negative 3 close  across each line.

6. the x-axis
7. y-axis
8. Δ W X Y cap delta w x y  has vertices W ( − 4 , 1 ) , X ( 2 , − 7 ) , and  Y ( 0 , − 3 ) . w open negative 4 comma 1 close comma x open 2 comma negative 7 close comma , and y open 0 comma negative 3 close .  What are the vertices of the image of Δ W X Y cap delta w x y  for the translation ( x , y ) → ( x − 3 , y + 5 ) ? open x comma y close rightwards arrow . open x minus 3 , comma . y plus 5 close question mark
9. Δ A B C cap delta eh b c  has vertices A ( − 1 , 4 ) , B ( 2 , 0 ) , and  C ( 4 , 3 ) . eh open negative 1 comma 4 close comma b open 2 comma 0 close comma , and c open 4 comma 3 close .  Graph the reflection image of Δ A B C cap delta eh b c  across the line x = − 1 . x equals . negative 1 .

Copy each figure and point A. Draw the image of each figure for the given angle of rotation about A. Use prime notation to label the vertices of the image.

10. 40 ° 40 degrees

    

11. 90 ° 90 degrees

    

12. How many lines of symmetry does a regular pentagon have? Include a sketch in your answer.

Tell what type(s) of symmetry each figure has. For line symmetry, sketch the image and the line(s) of symmetry. For rotational symmetry, state the angle of rotation.

Do you UNDERSTAND?

15. Reasoning The point ( 5 , − 9 ) open 5 comma negative 9 close  is the image under the translation ( x , y ) → ( x − 3 , y + 2 ) . open x comma y close rightwards arrow . open x minus 3 , comma . y plus 2 close .  What is its preimage?
16. Reasoning The point T ( 5 , − 1 ) t open 5 comma negative 1 close  is reflected first across the x-axis and then across the y-axis. What is the distance between the image and the preimage? Explain.
17. Coordinate Geometry The point L(a, b) in Quadrant I is rotated 90 ° 90 degrees  about the origin and then reflected across the y-axis. What are the coordinates of the image of L?

The two letters in each pair are congruent. Does one figure appear to be a translation image, a reflection image, or a rotation image of the other?

18. 
19. 

20. Error Analysis Your friend draws the diagram below to show the reflection of ▱ white parallelogram PQRS across the x-axis. Explain and correct your friend's error.

    

Table of Contents