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Transformations

Transformations. Math 8. Four Types. Translation (Slide) Rotation (turn) Reflection (flip) Dilation (shrinking/stretching). Examples:. When working with transformations it is helpful to remember the coordinate system. Quadrant 1 (+x, +y) Quadrant 2 (-x, +y) Quadrant 3 (-x, -y)

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Transformations

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  1. Transformations Math 8

  2. Four Types • Translation (Slide) • Rotation (turn) • Reflection (flip) • Dilation (shrinking/stretching)

  3. Examples:

  4. When working with transformations it is helpful to remember the coordinate system Quadrant 1 (+x, +y) Quadrant 2 (-x, +y) Quadrant 3 (-x, -y) Quadrant 4 (+x, -y)

  5. Examples:

  6. Reflections-(Flip) • When you reflect a shape in the coordinate plane, you reflect it over a line. This line is called the line of reflection/symmetry. • When a figure is reflected on a coordinate plane, every point of the figure must have a corresponding point on the other side.

  7. Most reflections are over the x-axis (horizontal), the y-axis (vertical), or the line y = x (diagonal uphill from left to right.)

  8. Reflections • When you reflect a shape over the x –axis, use the same coordinates and multiply the y coordinate by –1. (x, opposite y) • When you reflect a shape over the y-axis, use the same coordinates and multiply the x coordinate by –1. (opposite x, y) • When you reflect a shape over the line y=x, use the same coordinates and multiply both by –1.

  9. Examples: • 1. Reflect the triangle over the x-axis and y – axis.

  10. Examples:

  11. Examples:

  12. Translations (Slides/Glide) • To translate a figure in the direction describe by an ordered pair, add the ordered pair to the coordinates of each vertex of the figure. • The new set of ordered pairs is called the image. It is shown by writing A’. This is read the image of point A.

  13. Examples • Find the coordinates of the vertices of each figure after the translation described. Use the graph to help you.

  14. Examples: • Find the coordinates of the vertices of each figure after the translation described.

  15. Rotations (Turns) • ·¼ turn = 90 degrees rotation • ·½ turn = 180 degrees rotation • ·¾ turn = 270 degrees rotation • ·full turn = 360 degrees rotation Example: Example:

  16. In the coordinate plane we have 4 quadrants. If the shape is rotated around (0,0) then: • 90 degrees rotation moves 1 quadrant • Rotating 90 clockwise. (x, y) (y, opposite x) same as 270 counterclockwise. • Rotating 90 counterclockwise is the same as 270 clockwise. (x, y) (opposite y, x) • 180 degrees rotation moves 2 quadrants • Multiply both by – 1. • (x, y,)  (opposite x, opposite y) • 270 degrees rotation moves 3 quadrants • Rotating 270 counterclockwise is the same as 90 clockwise • (x, y) (y, opposite x) • 360 degrees rotation moves 4 quadrants • (stays the same)

  17. Examples: • If a triangle is in Quadrant 2 and is rotated 270 counterclockwise, what quadrant is it now in? • If a triangle is in Quadrant 4 and is rotated 90 clockwise, what quadrant is it now in?

  18. Symmetry Two Types: 1. Line Symmetry (can be called reflectional symmetry)– if you can fold a shape and have the edges meet • The place where you fold is called the line of symmetry

  19. More Line Symmetry

  20. InkBlots

  21. Does the Human Face Possess Line Symmetry?

  22. Answer: No

  23. Girl

  24. Carpets

  25. Examples: • Do the following shapes have line symmetry? If so, how many lines of symmetry do they have? a. b. c. d. e.

  26. Rotational Symmetry • 2. Rotational Symmetry: If you can turn the shape less than 360o and still have the same shape. • Order of Rotational Symmetry: Is the number of rotations that must be made to return to the original orientation • Minimum Rotational Symmetry: The smallest number of degrees a shape can be rotated and fit exactly on itself • Hint: Take 360o divided by the number of sides/points.

  27. Examples:

  28. Examples: Does the following shape have rotational symmetry? If yes, what is the order and MRS? a. b. c. d. e.

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