ganeshie8
  • ganeshie8
Is it possible to flip a shape using below transformations : 1) translate 2) rotate about a point 3) scale about a point
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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starwars18
  • starwars18
If by scale you mean change size, then I don't believe so.
UsukiDoll
  • UsukiDoll
well we can use isometric transformations... but translate does nothing to a shape.
ganeshie8
  • ganeshie8
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..

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starwars18
  • starwars18
You can't flip a shape like in actuality, but you may be able to rotate it so it seems like it has flipped
UsukiDoll
  • UsukiDoll
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.
UsukiDoll
  • UsukiDoll
isometry preserves shape
ganeshie8
  • ganeshie8
yeah i see.. so scaling is not useful, how can we achieve flip effect by rotating @starwars18
starwars18
  • starwars18
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...
ganeshie8
  • ganeshie8
|dw:1435835651970:dw|
starwars18
  • starwars18
ok nvrmind, my idea wouldn't work
ganeshie8
  • ganeshie8
consider above shape \(\color{blue}{F}\) I'd like to flip it over that red line \(y=x\)
UsukiDoll
  • UsukiDoll
let's see... there's reflection, rotation, glide reflection...
starwars18
  • starwars18
idk about this, and i gtg. good luck
ganeshie8
  • ganeshie8
Okay np, thanks for trying :)
UsukiDoll
  • UsukiDoll
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
ganeshie8
  • ganeshie8
interesting, the only tools available to me are `translation` and `rotation`
Sachintha
  • Sachintha
I think scale is useful. :D
UsukiDoll
  • UsukiDoll
no. We can't change the size otherwise it's a non isometric transformation and we don't want that.
Sachintha
  • Sachintha
But what happens if we scale down beyond the smallest size possible? Won't we get a flipped one? Just curious to know. :)
UsukiDoll
  • UsukiDoll
anyway @ganeshie8 the letter F was assigned ... oh wait now I remembered. I had to find the axis of symmetry
UsukiDoll
  • UsukiDoll
Isometric transformations preserve the angles and preimage. We can't change it's size. Isometry retains shape too.
ganeshie8
  • ganeshie8
@Sachintha do you mean negative scaling ?
UsukiDoll
  • UsukiDoll
on top of reflections and rotations ... or glide reflections if any @ganeshie8
Sachintha
  • Sachintha
Yeah ganeshie.
ganeshie8
  • ganeshie8
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
ganeshie8
  • ganeshie8
scaling x coordinates by -1 and y coordinates by 1 produces this |dw:1435837233886:dw| which is indeed a reflection over y axis
ganeshie8
  • ganeshie8
how do i go about reflecting over that red line ?
UsukiDoll
  • UsukiDoll
I got that reflection too ... for the y-axis
Sachintha
  • Sachintha
Translating and some rotating. I hope. :)
UsukiDoll
  • UsukiDoll
maybe reflect on the x-axis and somehow that would hit the red line.
UsukiDoll
  • UsukiDoll
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
ganeshie8
  • ganeshie8
scaling x coordinates by 1 and y coordinates by -1 produces this |dw:1435837471541:dw|
UsukiDoll
  • UsukiDoll
http://www.regentsprep.org/regents/math/geometry/gt0/trans2.gif translation for a triangle for example
Sachintha
  • Sachintha
How about taking it to the mirror position by translating along x and y axis. Then rotating 90 deg clockwise?
UsukiDoll
  • UsukiDoll
maybe .. hmm we can rotate that new F (the one reflected along the y-axis by a certain degree ... or try to
UsukiDoll
  • UsukiDoll
|dw:1435837576558:dw|
ganeshie8
  • ganeshie8
you mean something like below, then rotate ? |dw:1435837659455:dw|
UsukiDoll
  • UsukiDoll
oh yeah that too.
UsukiDoll
  • UsukiDoll
|dw:1435837729251:dw|
UsukiDoll
  • UsukiDoll
if we use the original F and rotate it a bit we can pass through that red line faster.
UsukiDoll
  • UsukiDoll
either rotation by a certain degree.... or reflection along the x-axis ?!?!
UsukiDoll
  • UsukiDoll
|dw:1435838121146:dw| reflection along the x axis... looks crummy ...