Work on this as a table! QUIETLY! Determine the slope of each line. 1. PQ 2. MN 3. MQ 4. NP 5. Which pair of lines are parallel? – 10 3 MN, RQ

WARM-UP In the figure, WXYZ  ABCD 1. Find XY. 2. Find mB. 3. Find CD. 4. Find mZ ° 8 90°

TRY THIS…. Determine if the following sets of points form a parallelogram. 1. (–3, 0), (1, 4), (6, 0), (2, –4)yes

TRANSFORMATIONS

Three Types of Transformations! translations rotations 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 thesetranslation

WARM- UP 1)What are the three types of transformations? A B C A. B. A B C D A’ B’ C’ D’ translation reflection A’A’ B’B’ C’C’ translation, rotation, reflection, 2) Identify which type of transformation is taking place below.

Identify each as a translation, rotation, reflection, or none of these. B C D E F C. D. A A’A’ B’B’ C’C’ D’D’ F’F’ E’E’ rotation none of these Try This: Example 1C & 1D

Additional Example 2A: Drawing Transformations Draw the image of the triangle after the transformation. A B C A. Translation along AB so that A’ coincides with B A’ B’ C’

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

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

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

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

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

WARM UP 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) We found the opposite of each coordinate.

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 When you reflect across the “X” you change the “Y” i.e. 1 to -1, When you reflect across the “Y”, you change the “X” – i.e. 1,1 becomes -1,1

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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) x y –2 2

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

C. Reflection across the x-axis Draw the image of a shape with vertices of (1, –2), (3, 2), (7, 3), and (6, –1) after each transformation. Try This: Example 3C x y –2 2 C. Reflection across the x-axis When you reflect across the “X” you change the “Y” i.e. 1 to -1, When you reflect across the “Y”, you change the “X” – i.e. 1,1 becomes -1,1

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

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 2