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I've been doing math all day and this is my last problem and I've never seen one like it before please help!!
@iambatman @jigglypuff314 @Preetha
Can you post the "illustrated motion?"
oooh! I didn't even see it yes I will @mathmate
So this is a clockwise rotation about the origin, right?
Sorry, counter-clockwise rotation about the centre of 90 degrees per frame.
There is a matrix for r90. Do you know it by heart, or do you use the general matrix to rotate angle \(\theta\)?
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
Have you done translation matrices?
no... the furthest I've gone is inverted matrices...
So you know how to multiply a matrix?
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.
R= cos(theta) -sin(theta) sin(theta) cos(theta)
so with this problem...?
and the points matrix would be x1 x2 x3 x4... xn y1 y2 y3 y4 ... yn
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.
Each multiplication will rotate Pn by 90 degrees, CCW.
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.
ok I'm a bit lost... how would I write the matrices?
They were both given earlier, R, and Pn. The multiplication is only RRRRP
oooh! alright I see. so how would the finished problem look?
Do you find the matrices? I did not format them.
yes I see, where you said the points matrix, and R
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?
(sorry for the sloppy formatting)
ok... the formatting is a little hard to follow but I think I get it...
so is that the answer to my problem?
Not yet, you need to create Pn to represent the 4 points, then you can do the rotations.
can you show me? @mathmate
you have been soooo extremely helpful I wish i could thank you more!
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!
can you show me what the matrix would look like?
I'm sorry I'm not very smart :(
|dw:1433211807693:dw| Dont understimate yourself! :)
oh boy... I'm lost :( can you show me the next one so I can see the changes?
0 -2 ... -1 -3... for all 4 points
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?
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.
I'm just going to leave it like that and get half credit, thank you for your help.