Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Translation, Reflection, Dilation, and Rotation

             course offered by
            www.winpossible.com
Translation, Reflection, Dilation, and Rotation

Translation

A transformation in which a geometric figure is moved to ano...
Translation, Reflection, Dilation, and Rotation (continued)

In the translation means ∆ABC to ∆A’B’C’,
                   ...
Translation, Reflection, Dilation, and Rotation (continued)

A translation has a horizontal component and a vertical compo...
Translation, Reflection, Dilation, and Rotation (continued)

Reflection

A transformation in which a geometric figure is r...
Translation, Reflection, Dilation, and Rotation (continued)




                   B                                      ...
Translation, Reflection, Dilation, and Rotation (continued)

Reflection in a vertical line:




Reflection in a horizontal...
Translation, Reflection, Dilation, and Rotation (continued)

Reflection in the x axis
The x coordinates are the same and t...
Translation, Reflection, Dilation, and Rotation (continued)

Reflection in the y axis
The y coordinates are the same and t...
Translation, Reflection, Dilation, and Rotation (continued)

Dilation
A transformation in which a figure is enlarged or re...
Translation, Reflection, Dilation, and Rotation (continued)

Rotation

A transformation in which a figure is rotated aroun...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

Translate the triangle 4 units left and 5 units dow...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

If the image of point C(0, -12) under a translation...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

Find the images of points A(2, 3), B(-5, 2) and C(-...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

Triangle ABC has coordinates A(-2, 0), B(6, 0), and...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

After a reflection in the x-axis, (10, -3) is the i...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

After a dilation, (45, 0) are the coordinates of th...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

Translate the triangle 1 unit right and 3 units up,...
Translation, Reflection, Dilation, and Rotation (continued)

Example:

Rotate the triangle in the figure 90° clockwise abo...
Winpossible is a rapidly growing e-learning company based in California and New
York. Winpossible's math courses employ it...
Upcoming SlideShare
Loading in …5
×

Translation, Dilation, Rotation, ReflectionTutorials Online

53,596 views

Published on

In these slides you will learn the concepts and the basics of Translation, Reflection, Dilation, and Rotation.
http://www.winpossible.com/lessons/Geometry_Translation,_Reflection,_Dilation,_and_Rotation.html

Published in: Education, Business
  • You can ask here for a help. They helped me a lot an i`m highly satisfied with quality of work done. I can promise you 100% un-plagiarized text and good experts there. Use with pleasure! ⇒ www.WritePaper.info ⇐
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • You'll notice the difference immediately when you make the switch from working with amateurs to working with professionals. I've been betting with these guys for more than three years and in that time I've made nearly £500,000! That's a life changing amount of money. If I can give you one piece of advice it's this – sign up and sign up NOW! Last time I was one of the last guys to grab a spot before Patrick closed the doors. If I hadn't gotten lucky that day I'd be half a million pounds poorer now and my life would be a hell of a lot different. ➢➢➢ https://w.url.cn/s/AYQ6fO0
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Have u ever tried external professional writing services like ⇒ www.HelpWriting.net ⇐ ? I did and I am more than satisfied.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Hi there! I just wanted to share a list of sites that helped me a lot during my studies: .................................................................................................................................... www.EssayWrite.best - Write an essay .................................................................................................................................... www.LitReview.xyz - Summary of books .................................................................................................................................... www.Coursework.best - Online coursework .................................................................................................................................... www.Dissertations.me - proquest dissertations .................................................................................................................................... www.ReMovie.club - Movies reviews .................................................................................................................................... www.WebSlides.vip - Best powerpoint presentations .................................................................................................................................... www.WritePaper.info - Write a research paper .................................................................................................................................... www.EddyHelp.com - Homework help online .................................................................................................................................... www.MyResumeHelp.net - Professional resume writing service .................................................................................................................................. www.HelpWriting.net - Help with writing any papers ......................................................................................................................................... Save so as not to lose
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • Grab 5 Free Shed Plans Now! Download 5 Full-Blown Shed Plans with Step-By-Step Instructions & Easy To Follow Blueprints! ☺☺☺ https://t.cn/A62YdZJg
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

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
  20. 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

×