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

- ganeshie8

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- starwars18

If by scale you mean change size, then I don't believe so.

- UsukiDoll

well we can use isometric transformations... but translate does nothing to a shape.

- 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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## More answers

- 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

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

isometry preserves shape

- ganeshie8

yeah i see.. so scaling is not useful,
how can we achieve flip effect by rotating @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

|dw:1435835651970:dw|

- starwars18

ok nvrmind, my idea wouldn't work

- ganeshie8

consider above shape \(\color{blue}{F}\)
I'd like to flip it over that red line \(y=x\)

- UsukiDoll

let's see... there's reflection, rotation, glide reflection...

- starwars18

idk about this, and i gtg. good luck

- ganeshie8

Okay np, thanks for trying :)

- 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

interesting,
the only tools available to me are `translation` and `rotation`

- Sachintha

I think scale is useful. :D

- UsukiDoll

no. We can't change the size otherwise it's a non isometric transformation and we don't want that.

- 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

anyway @ganeshie8 the letter F was assigned ... oh wait now I remembered. I had to find the axis of symmetry

- UsukiDoll

Isometric transformations preserve the angles and preimage. We can't change it's size. Isometry retains shape too.

- ganeshie8

@Sachintha do you mean negative scaling ?

- UsukiDoll

on top of reflections and rotations ... or glide reflections if any @ganeshie8

- Sachintha

Yeah ganeshie.

- 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

scaling x coordinates by -1 and y coordinates by 1 produces this
|dw:1435837233886:dw|
which is indeed a reflection over y axis

- ganeshie8

how do i go about reflecting over that red line ?

- UsukiDoll

I got that reflection too ... for the y-axis

- Sachintha

Translating and some rotating. I hope. :)

- UsukiDoll

maybe reflect on the x-axis and somehow that would hit the red line.

- 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

scaling x coordinates by 1 and y coordinates by -1 produces this
|dw:1435837471541:dw|

- UsukiDoll

http://www.regentsprep.org/regents/math/geometry/gt0/trans2.gif translation for a triangle for example

- Sachintha

How about taking it to the mirror position by translating along x and y axis. Then rotating 90 deg clockwise?

- UsukiDoll

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

- UsukiDoll

|dw:1435837576558:dw|

- ganeshie8

you mean something like below, then rotate ?
|dw:1435837659455:dw|

- UsukiDoll

oh yeah that too.

- UsukiDoll

|dw:1435837729251:dw|

- UsukiDoll

if we use the original F and rotate it a bit we can pass through that red line faster.

- UsukiDoll

either rotation by a certain degree.... or reflection along the x-axis ?!?!

- UsukiDoll

|dw:1435838121146:dw| reflection along the x axis... looks crummy ...