1. TuringTest Group Title

hmm... it looks like all the coordinates are changing from$(a,b)\to(-b,a)$I wonder what that means.

2. hugsandkisses Group Title

I wonder what that means too!

3. TuringTest Group Title

pretty sure meverett will tell you

4. meverett04 Group Title

Draw a picture of the original shape. Then like the previous one, draw four circles for W, X, Y and Z. We have the 180 degree rotation again. C is our answer

5. hugsandkisses Group Title

I dont understand the rotations thing though. is there a formula, or do I have to draw everytime?

6. meverett04 Group Title

I am a visual learner, I draw the picture every time. @Turing, do you have a formula?

7. TuringTest Group Title

When you see the coordinates change from... $(a,b)\to(-b,a)$that means.a means counter-clockwise rotation 90 degrees clockwise is this change$(a,b)\to(b,-a)$the opposite of course. 180deg is$(a,b)\to(-a,-b)$which is obvious if you think about it. So I guess I do...

8. hugsandkisses Group Title

Oh, I see

9. meverett04 Group Title

Why does this work Turing?

10. TuringTest Group Title

I can recall that only because I just did it yesterday The real formula is done with matrices, but gives the same result.

11. TuringTest Group Title

I will show you the actual formula...

12. hugsandkisses Group Title

thankyou

13. TuringTest Group Title

you don't want it hugsandkisses it is above your level sorry...

14. hugsandkisses Group Title

Haha, alright. thanks for trying though

15. TuringTest Group Title

this multiplication maps a vector onto itself:$(a,b)\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]$...

16. TuringTest Group Title

this one turns it 180 degrees$(a,b)\left[\begin{matrix}-1 & 0 \\ 0 & -1\end{matrix}\right]$

17. hugsandkisses Group Title

umm.. thanks for trying to explain it to me :P

18. TuringTest Group Title

here is 90 deg closkwise$(a,b)\left[\begin{matrix}0 & -1 \\ 1 & 0\end{matrix}\right]$and counter-clockwise is$(a,b)\left[\begin{matrix}0 & 1 \\ -1 & 0\end{matrix}\right]$

19. hugsandkisses Group Title

thanks again for trying sir!

20. meverett04 Group Title

Hmmm ... I have some reading to due .... thank you for the start ...

21. TuringTest Group Title

but for you hugs and kisses just use what I gave above. I actually gave you the answer is you put my posts together.

22. TuringTest Group Title

not the matrices The part with the arrows

23. hugsandkisses Group Title

the arrows thing was much easier, thanks a ton