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

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

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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.) Course Transformations Move the 9 to the first triangle.

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

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Course Transformations Vocabulary transformation translation rotation center of rotation reflection image

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Course 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.

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

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Course 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

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

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

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

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Course 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) A B C A B C x y – –4

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Course 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 A B C B A C x y – –4

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Course Transformations Check It Out: Example 2A X Y Z X Y Z x y – –4 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)

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Course Transformations Check It Out: Example 2A X Y Z Y X Z x y – –4 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

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Course 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. Translation 2 t units up, point H x y –2 2 H I K J H I K J H I K J H(0, 4)

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Course 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. 90° rotation around (0, 0), point I x y –2 2 H I K J H I K J I(2, –4)

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Course 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. 180° clockwise rotation around (0, 0), point A x y –2 2 A B C D B A C D A(–1, 2)

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Course 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. Translation 10 units left, point C x y –2 2 A B C D C(-3, 3) A B C D

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Course 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) 2. (2, 3), (5, 5), (1, –2), (5, –4) and (–2, 3), (–5, 5), (–1, –2), (–5, –4) translation reflection

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Course Transformations 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) 4. (4, 1), (1, 2), (4, 5), (1, 5) and (–4, –1), (–1, –2), (–4, –5), (–1, –5) none rotation Lesson Quiz: Part II

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