Unit 2 Review

Author:Cally Pausewang

Topic:Dilation, Geometry, Reflection, Rotation, Similarity Transformation or Similarity, Symmetry, Geometric Transformations, Translation

Write your answers in complete sentences on a seperate sheet of paper. Be sure to number your answers to correspond to the questions.

1. In your own words, describe the following: a) transformations b) translations c) reflections d) rotations e) dilations f) tesselations

Parallel, Perpendicular, and intersecting lines

State whether the lines are parallel, perpendicular, or intersecting. If the intersect, find the point of intersection. Give each line in standard and slope-intercept form. 2.

and

Write a function that is parallel and perpendicular to the following at the given point. 5.

6. a function that goes through points

and

. The parallel/perpendicular line goes through

Translations

7. Find the general rule for each image. The original figure is the red polygon ABCD. 8. For each general rule, describe in words the transformations that occur. 9. Move the orginal figure ABCD. What happens to the diagram? What conclusion can you draw from this change? 10. How can I find the distance between the orginal figure and any of its images? Are there multiple ways? If so, what are they? 11. Find the distance between the quadrilateral ABCD and any of its images.

Reflections

12. Give a general rule for each image from its original figure, triangle ABC. 13. Focus on the image A'''B'''C''', give another general rule aside from the one you previously gave.

Rotations

14. Write the general rules and coordinates when the original figure ABCD is rotated about the origin counterclockwise. 15. Clockwise? 16. Pay attention to point Z. The image A'B'C'D' is a result of rotating the the figure 90° counterclockwise around point Z. What's the general rule for this rotation? 17. What if we wanted to rotate the figure 180°, what would the general rule be? 270°?

Dilation

18. What're the general rules for each image? 19. What if I asked you to dilate the orginal triangle ABC by a factor of 1/3? What are the new coordinates? Enlargment or reduction? What about a factor of 9/4?

20. Given the coordinates J'(4,1), K'(-2,7), and L(0,3), what are the original coordinates when the scale factor is 4/3?

Symmetry

Explore rotational and reflectional symmetry throguh the link. Create images and reflect them across lines. Choose shpaes with rotational symmetry and discover their orders.

21. Draw one of the figures you created with relfectional symmetry. 22. Draw 3 of the figures you discovered with rotational symmetry. Give the order and magnitude. 23. Draw an example of relfectional symmetry, rotational symmetry, neither, and both. Give their orders and magnitude.

Tesselations

Below are some pictures created by M.C. Escher. A mathematician and artist specializing in illusions and tesselations. Answer the following questions concerning his work.

https://mcescher.com/gallery/symmetry/#iLightbox[gallery_image_1]/12

24. What type of transformation is used in this tessellation?

https://mcescher.com/gallery/symmetry/#iLightbox[gallery_image_1]/31

25. Is this an example of a tessellation that we're are doing in class? Why or why not?

26. What type of transformation is used in this tessellation?

M.C. Escher

Click on the picture which will take you to M.C. Escher's offical website. Answer the following questions concerning his life and artwork.

27. Visit his biography. When and where was he born? 28. When was his first art exhibit? 29. How many lithographs, woocuts, and wood engravings did he have? How many sketches? 30. What are 3 more interesting facts about him? 31. Visit his gallery. Choose one piece from each collection and tell me about it. What's going on in picture? If it as a date and title make sure to list those. 32. Find one more piece of art that is your favorite. Why is it your favorite?

Extra Credit

Give me a good joke or pun for some extra points. (Extra extra points if picture included)