Question

are negative numbers allowed for \(x,y\) scale factors ?

Answer 1

As in negative scale factor?

Answer 2

yes, for example
multiplying all the coordinates by "2", blows up the shape by a factor of 2

Answer 3

Yes, I remember reading about something similar, we just use left instead of right, down instead of up, etc for transformations at least.

Answer 4

It seems like it could be interpreted as a reflection, but this is a good question I've thought about this sort of thing a lot.

Answer 5

Yeah, I remember reading about it as well haha, with graphs and what not

Answer 6

See I know some things in math! Guess, I'm not entirely an idiot xD

Answer 7

yeah multiplying x coordinates by -1 is indeed a reflection about y axis

Answer 8

nobbody knows everything in math,
so by ur definition everybody is somewhat idiot lmao

Answer 9

Haha, you know everything but this would make everything upside down right

Answer 10

Yes, a reflection

Answer 11

I think in some sense, negative numbers are sorta just a special case of complex numbers. If we look at subtraction in a literal sense, we can never take anything away from nothing, so 0-x=0 could be defined in this way, or simply be undefined since it's nonsense.

But yeah, I guess when I think of reflection if we think of smoothly transitioning the scale factor from 2 to 1 to 1/2 to 0 to -1/2 to -1... we can sort of imagine a scale turning an object inside out through itself. So it depends on if you want to allow this sorta thing or not haha.

Answer 12

Multiplying both by -1 should flip them across both x and y axis.

Answer 13

wow! yeah it is useful to allow as we can use the same formula of scaling for reflection also... wonder if it can be extended for any arbitrary line ?

Answer 14

reflection over y axis : scale by (-1, 1)
reflection over x axis : scale by (1, -1)

reflection over y=-x : scale by (-1, -1)

Answer 15

reflection over y=mx may involve complicated expressions for scale factors i see

Answer 16

Looks below sequence of transformations work for reflection over any vertical line \(x=k\)

```
translate(x-k, 0)
scale(-1, 1)
translate(k, 0)
```

Answer 17

a good topic for chirality and enantiomers in molecular geometry

Answer 18

well, scale factors are SCALE means take | | for it , other wise negative is a reflection so
if you wanna scale by ( negative something, negative something)
the negative is a direction which might do (translate, reflection,rotate) and the something as scalar itself do the scale hmmm even though i cant see any harm in doing it why cant scale be both scalar and a movement ? (translate, reflection,rotate)
this is should be good in maps encryption.
do you have a special case or something ?

Answer 19

basically the tool im using has no reflection feature.
so im thinking of achieving it using below transformations

1) translation
2) scaling
3) rotation

Answer 20

oh you wanna reflection like symmetry or what ?
could you give an example ?

Answer 21

Are negative scale factors allowed for a homogeneous thing that doesn't change with zooming ?