5-7 Transformations Warm Up Problem of the Day Lesson Presentation Pre-Algebra

5-7 Transformations Warm Up Pre-Algebra 5-7 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. 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.

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

Vocabulary transformation translation rotation center of rotation reflection image

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.

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

Additional Example 1A & 1B: Identifying Transformations Identify each as a translation, rotation, reflection, or none of these. A. B. reflection rotation

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

Try This: Example 1A & 1B 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

Try This: Example 1C & 1D 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: Drawing Transformations Draw the image of the triangle after the transformation. A. Translation along AB so that A’ coincides with B A A’ B’ C’ B C

Additional Example 2B: Drawing Transformations Draw the image of the triangle after the transformation. B. Reflection across BC. A B A’ B’ C’ C

Additional Example 2C: Drawing Transformations Draw the image of the triangle after the transformation. A’ B’ C’ C. 90° clockwise rotation around point B A B C

Try This: Example 2A Draw the image of the polygon after the transformation. A’ B’ C’ D’ E’ F’ A. Translation along DE so that E’ coincides with D B C A F D E

Try This: Example 2B Draw the image of the polygon after the transformation. B. Reflection across CD. B A’ B’ C’ D’ E’ F’ C A F D E

Try This: Example 2C Draw the image of the polygon after the transformation. C. 90° counterclockwise rotation around point C C’ A’ B’ D’ E’ F’ B C A F D E

Additional Example 3A: Graphing Transformations Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation. A. 180° counterclockwise rotation around (0, 0)

Additional Example 3B: Graphing Transformations Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation. B. Translation 5 units left

Additional Example 3C: Graphing Transformations Draw the image of a triangle with vertices of (1, 1), (2, –2 ), and (5, 0) after each transformation. C. Reflection across the x-axis

A. 180° clockwise rotation around (0, 0) Try This: Example 3A Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. A. 180° clockwise rotation around (0, 0) y 2 x –2

B. Translation 10 units left Try This: Example 3B Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. B. Translation 10 units left y 2 x –2

C. Reflection across the x-axis Try This: Example 3C Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. C. Reflection across the x-axis y 2 x –2

Lesson Quiz: Part 1 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

Lesson Quiz: Part 2 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