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ganeshie8

  • one year ago

Is it possible to flip a shape using below transformations : 1) translate 2) rotate about a point 3) scale about a point

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  1. starwars18
    • one year ago
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    If by scale you mean change size, then I don't believe so.

  2. UsukiDoll
    • one year ago
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    well we can use isometric transformations... but translate does nothing to a shape.

  3. ganeshie8
    • one year ago
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    Like, I have access to those listed transformations only. I have been trying to flip a shape about a line using them but it seems almost impossible..

  4. starwars18
    • one year ago
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    You can't flip a shape like in actuality, but you may be able to rotate it so it seems like it has flipped

  5. UsukiDoll
    • one year ago
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    well we can't change the size.. that's a non isometric transformation. We don't want that. Isometric transformations preserve the preimage and the angles.

  6. UsukiDoll
    • one year ago
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    isometry preserves shape

  7. ganeshie8
    • one year ago
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    yeah i see.. so scaling is not useful, how can we achieve flip effect by rotating @starwars18

  8. starwars18
    • one year ago
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    can you cross the line by translation? if you can cross it, rotate so the same point that would be flipped touches the line, then translate it so it touches the line like it was flipped. i think...

  9. ganeshie8
    • one year ago
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    |dw:1435835651970:dw|

  10. starwars18
    • one year ago
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    ok nvrmind, my idea wouldn't work

  11. ganeshie8
    • one year ago
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    consider above shape \(\color{blue}{F}\) I'd like to flip it over that red line \(y=x\)

  12. UsukiDoll
    • one year ago
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    let's see... there's reflection, rotation, glide reflection...

  13. starwars18
    • one year ago
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    idk about this, and i gtg. good luck

  14. ganeshie8
    • one year ago
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    Okay np, thanks for trying :)

  15. UsukiDoll
    • one year ago
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    I think my class did this last semester . My professor assigned a bunch of letters and we had to find the glide reflections, reflections, rotations... if any

  16. ganeshie8
    • one year ago
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    interesting, the only tools available to me are `translation` and `rotation`

  17. Sachintha
    • one year ago
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    I think scale is useful. :D

  18. UsukiDoll
    • one year ago
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    no. We can't change the size otherwise it's a non isometric transformation and we don't want that.

  19. Sachintha
    • one year ago
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    But what happens if we scale down beyond the smallest size possible? Won't we get a flipped one? Just curious to know. :)

  20. UsukiDoll
    • one year ago
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    anyway @ganeshie8 the letter F was assigned ... oh wait now I remembered. I had to find the axis of symmetry

  21. UsukiDoll
    • one year ago
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    Isometric transformations preserve the angles and preimage. We can't change it's size. Isometry retains shape too.

  22. ganeshie8
    • one year ago
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    @Sachintha do you mean negative scaling ?

  23. UsukiDoll
    • one year ago
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    on top of reflections and rotations ... or glide reflections if any @ganeshie8

  24. Sachintha
    • one year ago
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    Yeah ganeshie.

  25. ganeshie8
    • one year ago
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    let me try scaling that F using scale factors of -1 along x and 1 along y that should reflect the object over y axis i guess

  26. ganeshie8
    • one year ago
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    scaling x coordinates by -1 and y coordinates by 1 produces this |dw:1435837233886:dw| which is indeed a reflection over y axis

  27. ganeshie8
    • one year ago
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    how do i go about reflecting over that red line ?

  28. UsukiDoll
    • one year ago
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    I got that reflection too ... for the y-axis

  29. Sachintha
    • one year ago
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    Translating and some rotating. I hope. :)

  30. UsukiDoll
    • one year ago
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    maybe reflect on the x-axis and somehow that would hit the red line.

  31. UsukiDoll
    • one year ago
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    if I remembered correctly translation is like F F F F F F F nothing happens. I used to know a site that did those pictures that showed all 8 isometric transformations

  32. ganeshie8
    • one year ago
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    scaling x coordinates by 1 and y coordinates by -1 produces this |dw:1435837471541:dw|

  33. UsukiDoll
    • one year ago
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    http://www.regentsprep.org/regents/math/geometry/gt0/trans2.gif translation for a triangle for example

  34. Sachintha
    • one year ago
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    How about taking it to the mirror position by translating along x and y axis. Then rotating 90 deg clockwise?

  35. UsukiDoll
    • one year ago
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    maybe .. hmm we can rotate that new F (the one reflected along the y-axis by a certain degree ... or try to

  36. UsukiDoll
    • one year ago
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    |dw:1435837576558:dw|

  37. ganeshie8
    • one year ago
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    you mean something like below, then rotate ? |dw:1435837659455:dw|

  38. UsukiDoll
    • one year ago
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    oh yeah that too.

  39. UsukiDoll
    • one year ago
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    |dw:1435837729251:dw|

  40. UsukiDoll
    • one year ago
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    if we use the original F and rotate it a bit we can pass through that red line faster.

  41. UsukiDoll
    • one year ago
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    either rotation by a certain degree.... or reflection along the x-axis ?!?!

  42. UsukiDoll
    • one year ago
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    |dw:1435838121146:dw| reflection along the x axis... looks crummy ...