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Warm up

Warm up. 1. Graph the following lines: y = 3 x = -4 y = 5 2. Graph the rectangle with points A(-8, 5), B(-2, 5), C(-8,1) and D(-2, 1). Reflect it over the line y = 3. What do you notice?. Unit 5 – Transformations in the Plane. Coordinate Algebra EOCT Review. Unit 5 - Transformations.

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Warm up

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  1. Warm up 1. Graph the following lines: • y = 3 • x = -4 • y = 5 2. Graph the rectangle with points A(-8, 5), B(-2, 5), C(-8,1) and D(-2, 1). Reflect it over the line y = 3. What do you notice?

  2. Unit 5 – Transformations in the Plane Coordinate AlgebraEOCT Review

  3. Unit 5 - Transformations • Represent transformations in the plane • Compare rigid and non-rigid • Translations • Rotations • Reflections • Understand Dilations

  4. Transformations are called RIGID if every image is congruent to its preimage. Rigid transformations can also be referred to as an ISOMETRY. Every segment is congruent to its image.

  5. Congruent Figures are congruent if they have the same shape, size, lines, and angles.

  6. Translations • Translate C(-4, 7) by (x – 7, y – 9). C’(-11, -2)

  7. Translate the image by (x – 8, y + 2)

  8. Find the pre-image(x + 12, y – 17)

  9. Reflections

  10. Reflections • Reflect C(-4, 7) across the line y = -x C’(-7, 4)

  11. Reflections • Reflect across the y-axis (-1, 2) (-1,-4) (-3, 1) (-3, -3)

  12. Reflections • Reflect across the x-axis, then across the line y = x L’’(-2, 1) G’’(-4,3) Q’’(1, 4)

  13. Reflections • Reflect across the line y = -1 (1, 2) (1,-4) (3, 1) (3, -3)

  14. Rotations

  15. Rotations • Rotate C(-4, 7) 90 degrees cw about the origin. C’(7, 4)

  16. Rotate 270 degrees cw about the origin C’(-4, -2)  A’(8, 0)  T’(-5, -3) 

  17. Rotations • Rotate 180 degrees, then 270 ccw about the origin. L’’(-2, 1) G’’(-4,3) Q’’(1, 4)

  18. Rotations • Rotate 270 cw about the point (1,1). L’’(-2, 1) G’’(-4,3) Q’’(1, 4)

  19. Compositions • Reflect across x = 2. • Rotate 180 degrees about the point (1,-1). (1, 2) (1,-4) (3, 1) (3, -3)

  20. Rotational Symmetry

  21. What is a line of symmetry? • A line on which a figure can be folded so that both sides match.

  22. Name each regular polygon.How many sides does each have? 5 4 3 These are known as orders of rotation The number of lines equal the number of sides 8 6

  23. Rotational Symmetry • Order of a Rotational Symmetry – The amount of times that an object fits on top of itself when being rotated. • Calculating Rotational Symmetries: • Find the Order of the Rotational Symmetry • Divide 360 ° by the Order of the Rotational Symmetry • This value represents the first Rotational Symmetry. • Continue adding this value to find the next Rotational Symmetry. • Add this value until you reach 360°.

  24. Practice finding Rotational Symmetries with your team! Rotational Symmetry Practice Order of Rotational Symmetry: 6 1 6 Calculate the Rotational Symmetries 360 ÷ 6 = 60° 5 2 List all Rotational Symmetries: (+60°) (+60°) (+60°) 180°, 120°, 60°, (+60°) (+60°) 240°, 360° 3 4 300°,

  25. State the order of rotational symmetry.List each angle of rotation.

  26. Degrees in a Circle 360° 0° 22.5° 315° 45° + 45° + 45° + 90° + 90° + 45° + 45° 270° 90° + 45° + 45° + 90° + 90° + 45° + 45° 135° 225° 180°

  27. . Determine the number of degrees it takes to rotate the image onto itself.

  28. Determine the number of degrees it takes to rotate the image onto itself.

  29. Dilations • NOT an isometry. • Dilations are a resizing of the image. They change the lengths of the segments but NOT the ANGLES.

  30. Use the given scale factor to find the coordinates of the vertices of the image of the polygon.

  31. Use the given scale factor to find the coordinates of the vertices of the image of the polygon.

  32. Closing Describe every transformation that maps the given figure to itself.

  33. Closing Describe every transformation that maps the given figure to itself.

  34. Practice Problems CW/HW

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