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- 1. Translation, Reflection, Dilation, and Rotation course offered by www.winpossible.com
- 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. 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. 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. 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. 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. Translation, Reflection, Dilation, and Rotation (continued) Reflection in a vertical line: Reflection in a horizontal line: Reflection in a diagonal line:
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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
- 20. Winpossible is a rapidly growing e-learning company based in California and New York. Winpossible's math courses employ its patented ChalkTalk method or unique ChalkTalkTM technology for presenting clear explanations on solving hundreds of problems of varying levels of difficulty. Our methodology helps accurately diagnose students’ performance levels, and allows them to focus content that is most relevant to them. For more info, lots of free content, access to free math-homework help and lots more on high-school math, please visit: www.winpossible.com

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