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Good Morning! Have your homework on your desk and a red pen.

Good Morning! Have your homework on your desk and a red pen. Take out your whiteboards and whiteboard pens . Take out a piece of graph paper and title your notes 12.1:Reflections S tart writing down the Learning Objective SWBAT identify and draw reflections. .

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Good Morning! Have your homework on your desk and a red pen.

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  1. Good Morning! • Have your homework on your desk and a red pen. • Take out your whiteboards and whiteboard pens. • Take out a piece of graph paper and title your notes 12.1:Reflections • Start writing down the Learning Objective • SWBAT identify and draw reflections.

  2. When are we ever going to have to use this? • Computer animations • http://www.youtube.com/watch?v=dVtz55mIuz4 • 0-1:37

  3. Whiteboards: Do Now • What transformation is suggested by the wings of an airplane? • What transformation is suggested by a person climbing a ladder? • What transformation is suggested by a Ferris wheel?

  4. Do Now! • On your whiteboard answer the following questions. • Identify the transformationand use arrow notation to describe the transformation.

  5. Do Now! • On your whiteboard answer the following questions. • 2. Identify the transformationand use arrow notation to describe the transformation.

  6. Do Now! • On your whiteboard answer the following questions. • 3. Identify the transformationand use arrow notation to describe the transformation.

  7. Do Now! • On your whiteboard answer the following questions. • 4. A figure has vertices at A(1, -1), B(2, 3), and C(4, -2). After a transformation, the image of the figure has vertices at A’(-1, -1), B’(-2, 3), and C’(-4, -2). • Draw the pre-image and image. • Identify the transformation. • Use arrow notation to describe the transformation.

  8. Check your work! Reflection: ABC A’B’C’

  9. Isometry • If I say that a reflected image is isometric to it’s pre-image, what do you think I mean? • Think-pair-share • Isometry • image of a reflected figure is congruentto the pre-image.

  10. 12-1 Reflections • Reflection – a transformation that moves the pre-image by flipping it across a line(Line of Reflection) • What do we call line LP in terms of reflection? • Line of Reflection

  11. 12-1 Reflections • Example 1 • Tell whether each transformation appears to be a reflection. Explain your answer using one to two complete sentences. Do this on your own; I should not hear any talking. • (a) • (b)

  12. 12-1 Reflections • The week before break, we created reflections with our names using a piece of white paper and tracing our name using the light from the window. • Today we are going to reflect images using patty paper or also known as tracing paper. • You will only be given one piece of patty paper. Please pay attention so you do not mess up. • Materials you will need: • A ruler • A pencil • An eraser

  13. 12-1 Reflections • Constructing a Reflection using Patty Paper • Draw a line, using your ruler, in the middle of your patty paper. Label this line the Line of Reflection. • Draw a figure on one side of the line of reflection. Make sure this figure has no curved edges and label it the pre-image. • Fold your patty paper along the line of reflection. • Trace your figure on the folded side. Label the figure the image. • Unfold the patty paper. You have a reflection!

  14. 12-1 Reflections • Now you were able to reflect using patty paper… • But, I’m just not convinced that this is a reflection. I am more of numbers person. Can you and your tablemates use numbers to convince me that this is a reflection? • Main Idea: • The distance from a point on the pre-image to the line of reflection is equal to the distance from the image to the line of reflection. • When you draw a line from a point on the pre-image to the reflected point on the image, the line is a perpendicular bisector to the line of reflection.

  15. 12-1 Reflections • Example 2 • With your tablemates, create a plan to reflect the triangle across the line using a pencil, eraser, and ruler ( NO PATTY PAPER!). • On one whiteboard, write steps that an elementary student could follow such that you teach them how to draw the image of the triangle.

  16. Copy the triangle and the line of reflection. Draw the reflection of the triangle across the line. Step 1 Through each vertex draw a line perpendicular to the line of reflection.

  17. Step 2 Measure the distance from each vertex to the line of reflection. Locate the image of each vertex on the opposite side of the line of reflection and the same distance from it.

  18. Step 3 Connect the images of the vertices.

  19. 12-1 Reflections • Example 3 – Attempt on your own • Reflect the figure with the vertices X(2, –1), Y(–4, –3), Z(3, 2) across the x-axis. • Use arrow notation to show the relationship between the pre-images ordered pair and the images ordered pair. For example, X(2, -1)  X’(?, ?). • What do you notice about the x and y values of the pre-image and image? • Discuss with your tablemates your solution. Do you all have the same idea? If not, provide evidence for your solution. • On one-two whiteboards write your tables solution. • Write legibly, random tables will be asked to share their whiteboard(s).

  20. Reflect the figure with the given vertices across the given line. X(2, –1), Y(–4, –3), Z(3, 2); x-axis The reflection of (x, y) is (x,–y). Y’ Z X’ X Z’ Y Graph the image and preimage.

  21. Reflecting Across the X-Axis • (x, y) (x, -y)

  22. 12-1 Reflections • Example 4 - Attempt on your own • Reflect the figure with the vertices D(2, 0), E(2, 2), F(5, 2), and G(5, 1) across y = x. • Use arrow notation to show the relationship between the pre-images ordered pair and the images ordered pair. • What do you notice about the x and y values of the pre-image and image? • Discuss with your tablemates your solution. Do you all have the same idea? If not, provide evidence for your solution. • On one-two whiteboards write your tables solution. • Write legibly, random tables will be asked to share their whiteboard(s).

  23. S’ T’ R S T R’ Reflecting Across y=x Reflect the figure with the given vertices across the given line. R(–2, 2), S(5, 0), T(3, –1); y = x The reflection of (x, y) (y, x).

  24. Reflecting across the y-axis • Talk with your table. • What do you think the image coordinates be if the pre-image is: • (x, y) 

  25. S V U T T’ U’ S’ V’ Whitebaords Reflect the rectangle with vertices S(3, 4), T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis. 1) What is the reflection rule? The reflection of (x, y) is (x,–y).

  26. Whiteboards Reflect the figure with the given vertices across the given line. 3.A(2, 3), B(–1, 5), C(4,–1); y = x A’(3, 2), B’(5,–1), C’(–1, 4) 4.U(–8, 2), V(–3, –1), W(3, 3); y-axis U’(8, 2), V’(3, –1), W’(–3, 3) 5.E(–3, –2), F(6, –4), G(–2, 1); x-axis E’(–3, 2), F’(6, 4), G’(–2, –1)

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