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7-7

7-7. Transformations. Warm Up. Problem of the Day. Lesson Presentation. Course 3. 7-7. Transformations. Course 3. Warm Up. Determine if the following sets of points form a parallelogram. 1 . (–3, 0), (1, 4), (6, 0), (2, –4). yes. 2 . (1, 2), (–2, 2), (–2, 1), (1, –2). no.

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7-7

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  1. 7-7 Transformations Warm Up Problem of the Day Lesson Presentation Course 3

  2. 7-7 Transformations Course 3 Warm Up Determine if the following sets of points form a parallelogram. 1. (–3, 0), (1, 4), (6, 0), (2, –4) yes 2. (1, 2), (–2, 2), (–2, 1), (1, –2) no 3. (2, 3), (–3, 1), (1, –4), (6, –2) yes

  3. 7-7 Transformations Course 3 Problem of the Day How can you move just one number to a different triangle to make the sum of the numbers in each triangle equal? (Hint: There do not have to be exactly 3 numbers in each triangle.) Move the 9 to the first triangle.

  4. 7-7 Transformations Course 3 Learn to transform plane figures using translations, rotations, and reflections.

  5. 7-7 Transformations Course 3 Vocabulary transformation translation rotation center of rotation reflection image

  6. 7-7 Transformations Course 3 When you are on an amusement park ride, you are undergoing a transformation. Ferris wheels and merry-go-rounds are rotations. Free fall rides and water slides are translations. Translations, rotations, and reflectionsare type of transformations.

  7. 7-7 Transformations Course 3 The resulting figure or image, of a translation, rotation or reflection is congruent to the original figure.

  8. 7-7 Transformations Reading Math A’ is read “A prime”. The point A is the image of point A. Course 3 Additional Example 1: Identifying Transformations Identify each as a translation, rotation, reflection, or none of these. B. A. rotation reflection

  9. 7-7 Transformations Course 3 Additional Example 1: Identifying Transformations Identify each as a translation, rotation, reflection, or none of these. C. D. none of the these translation

  10. 7-7 Transformations A’ C’ D’ A’ B’ B’ C’ Course 3 Check It Out: Example 1 Identify each as a translation, rotation, reflection, or none of these. A. B. B A A C D C B reflection translation

  11. 7-7 Transformations Course 3 Check It Out: Example 1 Identify each as a translation, rotation, reflection, or none of these. E’ C. D. A’ F’ D’ A B’ B C’ F C D none of these rotation E

  12. 7-7 Transformations Course 3 Additional Example 2A: Graphing Transformations Draw the image of the triangle with vertices A(1, 1), B(2, -2), and C(5, 0) after each transformation. A 180° counterclockwise rotation around (0, 0) y B’ 2 A x 0 C C’ 4 –2 2 –4 A’ –2 B

  13. 7-7 Transformations Course 3 Additional Example 2B: Graphing Transformations Draw the image of the triangle with vertices A(1, 1), B(2, -2), and C(5, 0) after each transformation. A reflection across the y-axis y 2 A’ A x 0 C C’ 4 –2 2 –4 –2 B B’

  14. 7-7 Transformations Course 3 Check It Out: Example 2A Draw the image of the triangle with vertices A(1, 2), B(2, –3), and Z(7, 0) after each transformation. A 180° counterclockwise rotation around (0, 0) y Y’ X 2 x 0 Z’ Z 4 –2 2 –4 –2 X’ Y

  15. 7-7 Transformations Course 3 Check It Out: Example 2A Draw the image of the triangle with vertices A(1, 2), B(2, -3), and Z(7, 0) after each transformation. A reflection across the y-axis y X’ X 2 x 0 Z’ Z 4 –2 2 –4 –2 Y’ Y

  16. 7-7 Transformations J’ J J K K’ K I I I’ H H H’ Course 3 Additional Example 3A: Describing Graphs of Transformations Rectangle HIJK has vertices H(0, 2), I(4, 2), J(4, 4), and K(0, 4). Find the coordinates of the image of the indicated point after each transformation. y Translation 2 t units up, point H H’(0, 4) x 2 –2

  17. 7-7 Transformations J K I H Course 3 Additional Example 3B: Describing Graphs of Transformations Rectangle HIJK has vertices H(0, 2), I(4, 2), J(4, 4), and K(0, 4). Find the coordinates of the image of the indicated point after each transformation. y 90° rotation around (0, 0), point I x I’(2, –4) ‘K ‘H 2 –2 ‘I ‘J

  18. 7-7 Transformations C A’ B D’ D B’ A C’ Course 3 Check It Out: Example 3A Parallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after each transformation. y 180° clockwise rotation around (0, 0), point A 2 x –2 A’(–1, 2)

  19. 7-7 Transformations C C B B D D A A Course 3 Check It Out: Example 3B Parallelogram ABCD has vertices A(1, –2), B(3, 2), C(7, 3), and D(6, –1). Find the coordinates of the images of the indicated point after each transformation. y Translation 10 units left, point C 2 x C’(-3, 3) –2

  20. 7-7 Transformations Course 3 Lesson Quiz: Part I Given the coordinates for the vertices of each pair of quadrilaterals, determine whether each pair represents a translation, rotation, reflection, or none of these. 1. (2, 2), (4, 0), (3, 5), (6, 4) and (3, –1), (5, –3), (4, 2), (7, 1) translation 2. (2, 3), (5, 5), (1, –2), (5, –4) and (–2, 3), (–5, 5), (–1, –2), (–5, –4) reflection

  21. 7-7 Transformations Course 3 Lesson Quiz: Part II Given the coordinates for the vertices of each pair of quadrilaterals, determine whether each pair represents a translation, rotation, reflection, or none of these. 3. (1, 3), (–1, 2), (2, –3), (4, 0) and (1, –3), (–1, 2), (–2, 3), (–4, 0) none 4. (4, 1), (1, 2), (4, 5), (1, 5) and (–4, –1), (–1, –2), (–4, –5), (–1, –5) rotation

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