Graphing and Describing Reflections
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1 Lesson: Graphing and Describing Reflections Day 4 Supplement Lesson Graphing and Describing Reflections Teacher Lesson Plan CC Standards 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Objective TSW Graph reflections. TSW Describe what happens to the coordinates when a reflection is performed. Mathematical Practices #1 Make sense of problems and persevere in solving them. #6 Attend to precision. #7 Look for and make use of structure. #8 Look for and express regularity in repeated reasoning. Note to teachers: Be sure to teach this lesson from the PowerPoint, not the student notes. You will be missing most of the lesson otherwise. Teacher Input Bellwork: Review bellwork. Homework: Review important problems assigned the previous night. Introduction: Introduce as directed on the PowerPoint. Lesson: Teach as directed in the PowerPoint. Be sure to look at the notes on each slide for additional instruction and answers. Practice Classwork Pages 5-6 Homework Pages 7-8 Closure See closure slide on PowerPoint. 1 P a g e
2 Student Notes Steps for Performing a Reflection Step 1: Step 2: Step 3: Start with any vertex and count the number of units to the specified axis or line. Measure the same distance on the other side of the specified axis (or line) and place a dot. Label using prime notation. Repeat for the other vertices. Example: Reflect figure ABCD across the y-axis. Pre-Image Image A(-6, 5) A (6, 5) B(-3, 5) B (3, 5) C(-3, 1) C (3, 1) D(-6, 3) D (6, 3) reflection across y-axis -----When you reflect across the y-axis----- The y-coordinate will always stay the same. The x-coordinate will always flip signs. x, y x, y Here is the same pre-image but this time it is reflected across the x-axis. Example: 2 P a g e
3 You Try #1 You Try #2 Reflect ABC across the y-axis Reflect figure QRST across the x-axis Name the coordinates of the image. Name the coordinates of the image. You Try #3 You Try #4 Reflect EFG across the line x=2 Reflect figure ABCD across the line y=4 Name the coordinates of the image. Name the coordinates of the image. 3 P a g e
4 You Try #5 You Try #6 Describe the reflection below. Describe the reflection below. You Try #7 You Try #8 Which of the following represents a Describe the below reflection. single reflection of Figure 1? You Try #9 4 P a g e
5 Name Date Period Classwork Reflections Directions: Perform each reflection. Label using prime notation. 1. Reflect over the x-axis. 2. Reflect over the y-axis. 3. Reflect across x = 1 4. Reflect across y = In a coordinate plane, triangle ABC has the verities A(-5, 1), B(-4, 4), and C(-3, 1). The triangle ABC is reflected across the x-axis, resulting in triangle A B C. Without graphing, what are the coordinates of A B C? A (, ) B (, ) C (, ) 5 P a g e
6 ABC has vertices A(2,1), B(3,-5), and C(-2,4). Graph ABC and its image A B C, after a reflection over each line below. Then, name the coordinates of A,B and C. 6. the x-axis 7. the y-axis 8. the horizontal line y=2 Describe each reflection below Which of the below describes a reflection of the point (9,7) across the y-axis? A. (9, 7) ( 9, 7) B. (9, 7) (9, 7) Explain how you know. 6 P a g e
7 Name Transformations Answer each of the following questions on transformations. 1) Translate WXYZ: 4 units to the right and 2 units down Label the image W X Y Z Name the coordinates of the pre-image and image: Homework Date Period W (, ) X (, ) Y (, ) Z (, ) W (, ) X (, ) Y (, ) Z (, ) 2) Reflect ABC over the x-axis. Label the image A B C Name the coordinates of the pre-image and image: A (, ) A (, ) B (, ) B (, ) C (, ) C (, ) 3) Write the coordinates of CDE. If CDE is reflected over the y-axis to form C D E what would be the coordinates of C D E? C (, ) D (, ) E (, ) C (, ) D (, ) E (, ) 7 P a g e
8 4) Which explanation indicates how Point A (-5,4) becomes Point A (1,2)? A. Move Point A 6 units to the left and 1 unit up B. Move Point A 3 units to the right and 1 unit down C. Move Point A 6 units to the right and 2 units down D. Move Point A 7 units to the left and 2 units down 5) Which of the following statements correctly explains how to perform a reflection of a figure on the coordinate plane? A. Turn the figure clockwise by the specified number of degrees. B. Slide the figure the specified number of units. C. Turn the figure counter-clockwise by the specified number of degrees. D. Flip the figure over the specified line of reflection. 6) What is the degree of rotation counter-clockwise from the pre-image to figure 2? What is the degree of rotation clockwise from the pre-image to figure 1? What is the degree of rotation counter-clockwise from the pre-image to figure 1? What is the degree of rotation counter-clockwise from the pre-image to figure 3? 7) The diagram on the right shows dilation. Was the original figure enlarged or reduced? Explain how you know. 8 P a g e
9 9 P a g e
10 Answer Key Graphing and Describing Reflections Student Notes Steps for Performing a Reflection Step 1: Step 2: Step 3: Start with any vertex and count the number of units to the specified axis or line. Measure the same distance on the other side of the specified axis (or line) and place a dot. Label using prime notation. Repeat for the other vertices. Example: Reflect figure ABCD across the y-axis. Pre-Image Image A(-6, 5) A (6, 5) B(-3, 5) B (3, 5) C(-3, 1) C (3, 1) D(-6, 3) D (6, 3) reflection across y-axis -----When you reflect across the y-axis----- The y-coordinate will always stay the same. The x-coordinate will always flip signs. x, y x, y Here is the same pre-image but this time it is reflected across the x-axis. Example: 10 P a g e
11 You Try #1 You Try #2 Reflect ABC across the y-axis Reflect figure QRST across the x-axis Name the coordinates of the image. A (2,3) B (8,6) C (4,7) Name the coordinates of the image. Q (-8,2) R (-4,2) S (-10,5) T (-6,5) You Try #3 You Try #4 Reflect EFG across the line x=2 Reflect figure ABCD across the line y=4 Name the coordinates of the image. Name the coordinates of the image. E (-1,-4) A (-9, 1) F (-4,-1) B (-5,1) G (-4,-4) C (-6,3) D (-9,3) 11 P a g e
12 You Try #5 You Try #6 Describe the reflection below. Describe the reflection below. Reflection across x-axis Reflection across y-axis You Try #7 You Try #8 Which of the following represents a Describe the below reflection. single reflection of Figure 1? You Try #9 12 P a g e
13 Name Answer Key Date Classwork Period Reflections Directions: Perform each reflection. Label using prime notation. 1. Reflect over the x-axis. 2. Reflect over the y-axis. 3. Reflect across x = 1 4. Reflect across y = In a coordinate plane, triangle ABC has the verities A(-5, 1), B(-4, 4), and C(-3, 1). The triangle ABC is reflected across the x-axis, resulting in triangle A B C. Without graphing, what are the coordinates of A B C? A ( -5, -1 ) B ( -4, -4 ) C (-3, -1 ) x-coordinate stays the same; y-coordinate flips signs. 13 P a g e
14 ABC has vertices A(2,1), B(3,-5), and C(-2,4). Graph ABC and its image A B C, after a reflection over each line below. Then, name the coordinates of A,B and C. 6. the x-axis 7. the y-axis 8. the horizontal line y=2 Describe each reflection below Reflection across x-axis Reflection across y = Which of the below describes a reflection of the point (9,7) across the y-axis? A. (9, 7) ( 9, 7) B. (9, 7) (9, 7) Explain how you know. A because the y-coordinate stayed the same and the x-coordinate flipped signs. 14 P a g e
15 Homework Name Answer Key Date Period Transformations Answer each of the following questions on transformations. 1) Translate WXYZ: 4 units to the right and 2 units down Label the image W X Y Z Name the coordinates of the pre-image and image: W ( -4, 4 ) X ( 4, 8 ) Y ( 4, -4 ) Z ( -4, -8 ) W ( 0, 2 ) X ( 8, 6 ) Y ( 8, -6 ) Z ( 0, -10 ) 2) Reflect ABC over the x-axis. Label the image A B C Name the coordinates of the pre-image and image: A ( 2, 3 ) A ( 2, -3 ) B ( 7, -3 ) B ( 7, -3 ) C ( 4, -6 ) C ( 4, -6 ) 3) Write the coordinates of CDE. If CDE is reflected over the y-axis to form C D E what would be the coordinates of C D E? C ( -4, -1 ) D ( 0, 3 ) E ( -3, 3 ) C ( 4, -1 ) D ( 3, 0 ) E ( 3, 3 ) 15 P a g e
16 4) Which explanation indicates how Point A (-5,4) becomes Point A (1,2)? A. Move Point A 6 units to the left and 1 unit up B. Move Point A 3 units to the right and 1 unit down C. Move Point A 6 units to the right and 2 units down D. Move Point A 7 units to the left and 2 units down 5) Which of the following statements correctly explains how to perform a reflection of a figure on the coordinate plane? A. Turn the figure clockwise by the specified number of degrees. B. Slide the figure the specified number of units. C. Turn the figure counter-clockwise by the specified number of degrees. D. Flip the figure over the specified line of reflection. 6) What is the degree of rotation counter-clockwise from the pre-image to figure 2? _180_ What is the degree of rotation clockwise from the pre-image to figure 1? 90 What is the degree of rotation counter-clockwise from the pre-image to figure 1? 270 What is the degree of rotation counter-clockwise from the pre-image to figure 3? 90 7) The diagram on the right shows dilation. Was the original figure enlarged or reduced? Explain how you know. The new image is referenced with prime symbols. The image became smaller so it would be considered a reduction of the pre-image. 16 P a g e
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