Translation, Dilation, Rotation, ReflectionTutorials Online

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In these slides you will learn the concepts and the basics of Translation, Reflection, Dilation, and Rotation.
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Translation, Dilation, Rotation, ReflectionTutorials Online

  1. 1. Translation, Reflection, Dilation, and Rotation course offered by www.winpossible.com
  2. 2. Translation, Reflection, Dilation, and Rotation Translation A transformation in which a geometric figure is moved to another location without any change in size or orientation. Every translated figure, called the image of the original figure, is congruent to original figure. Example: before translation after translation
  3. 3. Translation, Reflection, Dilation, and Rotation (continued) In the translation means ∆ABC to ∆A’B’C’, A’ B’ Point A has moved to A’ Point B has moved to B’ Point C has moved to C’ A C’ ∴ AA’ = BB’ = CC’ and AA’ || BB’ || CC’ B ∴∆ABC ≅ ∆A’B’C’ C
  4. 4. Translation, Reflection, Dilation, and Rotation (continued) A translation has a horizontal component and a vertical component. If movement with respect to the x-axis is l units and movement with respected to the y-axis is m units, then for any point A(x, y), its coordinates become A’(x + l, y + m). Example: Translate ∆ABC, 6 units left and 6 units down. y 5 A (3, 4) 4 3 B (5, 3) 2 1 C (1, 1) -5 -4 -3 -2 -1 1 2 3 4 5 x -1 A’ (-3, -2) -2 -3 B’ (-1, -3) (-5, -5) -4 C’
  5. 5. Translation, Reflection, Dilation, and Rotation (continued) Reflection A transformation in which a geometric figure is reflected across a line, creating a mirror image. The line is called the line of reflection. Example: Axis of reflection
  6. 6. Translation, Reflection, Dilation, and Rotation (continued) B B’ A A’ C C’ k A is fixed point on line of reflection. B’ is reflection of B in line k(B B’) C’ is reflection of C in line k(C C’)
  7. 7. Translation, Reflection, Dilation, and Rotation (continued) Reflection in a vertical line: Reflection in a horizontal line: Reflection in a diagonal line:
  8. 8. Translation, Reflection, Dilation, and Rotation (continued) Reflection in the x axis The x coordinates are the same and the y coordinates are the opposite. y 5 4 A (1, 3) 3 C(3, 2) 2 1 B (1, 1) -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4
  9. 9. Translation, Reflection, Dilation, and Rotation (continued) Reflection in the y axis The y coordinates are the same and the x coordinates are the opposite. y 4 A’ (-1, 3) A (1, 3) 3 C(5, 2) 2 C’ (-5, -2) 1 B’ (-1, 1) B (1, 1) -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4
  10. 10. Translation, Reflection, Dilation, and Rotation (continued) Dilation A transformation in which a figure is enlarged or reduced with respect to a point called the center of dilation. Dilation of a Geometric Figure A transformation in which all dimensions are lengthened or shortened by a common scale factor. C 2 4 The smaller figure above is dilated with a scale factor of 2 and a center of dilation C to produce the larger figure.
  11. 11. Translation, Reflection, Dilation, and Rotation (continued) Rotation A transformation in which a figure is rotated around a given point called the center of rotation by a specified degree measure in a specified direction. Example: before rotation angle of rotation = 90° clockwise after rotation center
  12. 12. Translation, Reflection, Dilation, and Rotation (continued) Example: Translate the triangle 4 units left and 5 units down. 5 y C(5, 5) A (2, 4) 4 3 2 1 B (3, 1) -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4
  13. 13. Translation, Reflection, Dilation, and Rotation (continued) Example: If the image of point C(0, -12) under a translation is C'(-5, -9), find the coordinates of the image of point E(7, -8) under the same translation.
  14. 14. Translation, Reflection, Dilation, and Rotation (continued) Example: Find the images of points A(2, 3), B(-5, 2) and C(-1, 4) after a reflection in the x-axis. y (-1, 4) C 4 3 A(2, 3) B(-5, 2) 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 x -1 -2 -3 -4
  15. 15. Translation, Reflection, Dilation, and Rotation (continued) Example: Triangle ABC has coordinates A(-2, 0), B(6, 0), and C(4, 0). Find the coordinates of the images of the vertices of the triangle after a reflection in the y-axis.
  16. 16. Translation, Reflection, Dilation, and Rotation (continued) Example: After a reflection in the x-axis, (10, -3) is the image of point E. What is the original location of point E?
  17. 17. Translation, Reflection, Dilation, and Rotation (continued) Example: After a dilation, (45, 0) are the coordinates of the image of a point with coordinates (5, 0). What are the coordinates of the image of (10, 25) after the same dilation?
  18. 18. Translation, Reflection, Dilation, and Rotation (continued) Example: Translate the triangle 1 unit right and 3 units up, then rotate the image 180° clockwise about the origin. y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8
  19. 19. Translation, Reflection, Dilation, and Rotation (continued) Example: Rotate the triangle in the figure 90° clockwise about the origin. y 8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 x -2 -4 -6 -8
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