1. anonymous

2. anonymous

@amistre64

3. anonymous

I've been doing math all day and this is my last problem and I've never seen one like it before please help!!

4. anonymous

@iambatman @jigglypuff314 @Preetha

5. mathmate

Can you post the "illustrated motion?"

6. anonymous

oooh! I didn't even see it yes I will @mathmate

7. anonymous

8. mathmate

So this is a clockwise rotation about the origin, right?

9. mathmate

Sorry, counter-clockwise rotation about the centre of 90 degrees per frame.

10. anonymous

counter-clocwise right?

11. anonymous

right

12. mathmate

There is a matrix for r90. Do you know it by heart, or do you use the general matrix to rotate angle $$\theta$$?

13. anonymous

I've never done rotated matrices before! I never learned it I don't know why they gave me this problem... please just show me step by step how you would do it

14. mathmate

Have you done translation matrices?

15. anonymous

no... the furthest I've gone is inverted matrices...

16. mathmate

So you know how to multiply a matrix?

17. anonymous

yes

18. mathmate

A rotation matrix R (in 2d) is a 2x2 matrix, when premultiplied to a 2x n matrix will rotate the n sets of coordinates by an angle theta.

19. anonymous

ok

20. mathmate

R= cos(theta) -sin(theta) sin(theta) cos(theta)

21. anonymous

oh ok

22. anonymous

so with this problem...?

23. mathmate

and the points matrix would be x1 x2 x3 x4... xn y1 y2 y3 y4 ... yn

24. anonymous

alright

25. mathmate

We'll call the points matrix Pn (for n points). So create the R matrix for +90 degrees, and the P matrix for the pattern required.

26. mathmate

Each multiplication will rotate Pn by 90 degrees, CCW.

27. mathmate

For eight frames, you will multiply eight times. so RRRRPnPnPnPn with bring you back to the original position. Do that again will give you 8 frames.

28. anonymous

ok I'm a bit lost... how would I write the matrices?

29. mathmate

They were both given earlier, R, and Pn. The multiplication is only RRRRP

30. anonymous

oooh! alright I see. so how would the finished problem look?

31. mathmate

Do you find the matrices? I did not format them.

32. anonymous

yes I see, where you said the points matrix, and R

33. mathmate

So to rotate 90 degrees, it's RP,. Say $$P=(2,1)^T$$ and R 90 = 0 -1 1 0 by subst. cos(90) and sin(90). So multiply 0 -1 1 0 by 2 1 you'll get -1 2 get the idea?

34. mathmate

(sorry for the sloppy formatting)

35. anonymous

ok... the formatting is a little hard to follow but I think I get it...

36. anonymous

so is that the answer to my problem?

37. anonymous

@mathmate ?

38. mathmate

Not yet, you need to create Pn to represent the 4 points, then you can do the rotations.

39. anonymous

can you show me? @mathmate

40. anonymous

better formatting like this?

41. anonymous

you have been soooo extremely helpful I wish i could thank you more!

42. mathmate

The shape is made up of 4 points at frame 1. You make a 2x4 matrix to represent the 4 points, then premultiply by R, you'd get frame 2. But check the results!

43. anonymous

can you show me what the matrix would look like?

44. anonymous

I'm sorry I'm not very smart :(

45. mathmate

|dw:1433211807693:dw| Dont understimate yourself! :)

46. anonymous

oh boy... I'm lost :( can you show me the next one so I can see the changes?

47. mathmate

0 -2 ... -1 -3... for all 4 points

48. anonymous

I'm so sorry to ask this... and you can of course say no, but I'm supposed to show my work, its late, I've been doing math literally all day... could you please show me what the answer / end result would look like so I can be done?

49. mathmate

I am sorry I cannot do that. But I think you are able to solve the problem if you can identify the vertices of the shape, and do matrix multiplication. I can help you check when you finish, or attempted.

50. anonymous

I'm just going to leave it like that and get half credit, thank you for your help.

51. mathmate

Sorry! :(