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

7-7 Transformations Warm Up Course 3 7-7 Transformations 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

Move the 9 to the first triangle. Course 3 7-7 Transformations 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.

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

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

7-7 Transformations When you are on an amusement park ride, Course 3 7-7 Transformations 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 reflections are type of transformations.

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

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

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

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

7-7 Transformations Check It Out: Example 1 Course 3 7-7 Transformations 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 rotation none of these E

Additional Example 2A: Graphing Transformations Course 3 7-7 Transformations 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 C’ C –4 –2 2 4 A’ –2 B

Additional Example 2B: Graphing Transformations Course 3 7-7 Transformations 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 C’ C –4 –2 2 4 –2 B B’

7-7 Transformations Check It Out: Example 2A Course 3 7-7 Transformations 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 Z’ –4 –2 2 4 Z –2 X’ Y

7-7 Transformations Check It Out: Example 2A Course 3 7-7 Transformations 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 Z’ –4 –2 2 4 Z –2 Y’ Y

Additional Example 3A: Describing Graphs of Transformations Course 3 7-7 Transformations 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’ I’ K’ J’ H I K J H I K J H’(0, 4) x –2 2

Additional Example 3B: Describing Graphs of Transformations Course 3 7-7 Transformations 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 H I K J I’(2, –4) x ‘H ‘K –2 2 ‘I ‘J

7-7 Transformations Check It Out: Example 3A Course 3 7-7 Transformations 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 A B C D B’ A’ C’ D’ 2 x A’(–1, 2) –2

7-7 Transformations Check It Out: Example 3B Course 3 7-7 Transformations 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 A B C D A B C D 2 x C’(-3, 3) –2

7-7 Transformations Lesson Quiz: Part I Course 3 7-7 Transformations 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

7-7 Transformations Lesson Quiz: Part II Course 3 7-7 Transformations 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