# Is it possible to reflect/translate/dilate several objects at once?

Oliver Chamberlain shared this question 3 years ago

Hello,

Is it possible to reflect/translate/dilate several objects at once? If for example I have several arcs and segments forming a continuous design, is it possible for me to reproduce that entire design at once, rather than one element at a time?

Thanks

P.S. I hope I've made sense - as a stonemason, most of my geometry is visual and I don't understand much of the maths =/

1

Yes, you can use lists for example if 'a' and 'b' are an arc and a segment

1. Reflect[{a, b}, y = x]

or you can do it in two steps

1. list1 = {a,b}
2. Reflect[list1, y=x]

We can help with the maths, just ask!

Can you share any of your design work in GeoGebra? Would be cool to see :)

1

Thanks Michael, I should have asked this earlier before I put all the crockets on my pinnacle!

Once I'm done I'll share the design, (usually I do everything with a compass and straight edge so I don't have anything else to share at the moment).

1

So I'm hoping to take you up on that Maths help if its still there.

I'm trying to work out how to calculate where I should place a point so that when I dilate something from it, it comes out where I want. I managed to do it yesterday when reducing in scale, but I can't work out a point for enlarging.

I'm currently trying to enlarge something by a factor of b_8/i_8, and move it a distance j_8, (I'm using segments to measure the lengths), from point W_4 to point F_3. How do I calculate the centre of the point?

1

Can you post your .ggb file, or a simple example. I don't understand precisely what you want.

(maybe something like enlarging with scale factor of the reciprocal of b_8/i_8 ie i_8/b_8)

1

I've attached the file I'm working on. I'm trying enlarge one of the crockets so that it comes out at the top line. (I'm using the one on the bottom right because I can't get the others to dilate, maybe because they are lists?) Afterwards I'll try to rotate it so it stands upright.

Thanks for the help

1

I looked at this again with fresh eyes and actually managed to calculate the point (F_6) I was looking for. I do have a new problem though. Is it possible to stretch an object along one axis only? I'd like to distort the crocket by a factor of root2, stretching it along the x axis but maintaining the y values (as though viewed from an angle of 45). Again, I'm sorry if I'm struggling to make a coherent question.

1

Try:

1. Shear[c, xAxis, sqrt(2)]

If that's not right, just ask again!

1

ps also Stretch (but I think Shear is what you want)

https://www.geogebra.org/ma...

1

Thanks Michael, Stretch was actually what I needed. I am having problems using some of these functions with lists however, and have resorted to stretching/dilating one object at a time. Perhaps I'm doing something wrong?

A slightly different problem: Is it possible to draw/select part of a curve which isn't part of a circle? A hyperbola, ellipse, or a curve which I've previously stretched for example.

1

I found this: https://www.geogebra.org/he... but I can't get it to work. The file is attached, and e_{15} is the offending curve. I believe it is technically part of an ellipse but I hit rocks for a living so... :D

(I have also discovered that it isn't yet possible to do arcs for a parabola or hyperbola . Sorry for repeating questions asked elsewhere - I had tried looking but didn't have quite the right search terms).