Conversion Between Coordinate Systems
Hello, I've been stuck on this problem for awhile and I've tried googling up some solutions but I still cannot find an answer to this question.
1. The problem statement, all variables and given/known data An xy coordinate system is shown below. A second system, uv, is also shown. What is the relationship between the ucoordinate and the xcoordinate? https://www.vista.ubc.ca/webct/Relat...ractice8q.gif A. u = 0.57x + 3.44 B. u = 0.57x  3.44 C. u = 1.74x + 10.44 D. u = 1.74x  10.44 E. None of the above 2. Relevant equations I am not quite sure which equations are relevant but I think it has to do with linear transformations because of the rotating axes. 3. The attempt at a solution I have tried applying the rotation matrix with a theta of 125 deg which gives me [cos(125deg) sin(125deg) sin(125deg) cos(125deg)] and I find that the x coordinate of the resulting transformation is T(x) = x*cos(125)  y*sin(125). Since in the question, it asks for the x coordinate only, I would assume that y = 0. After, I subbed (x6) into x to translate the coordinate to match the picture. So my final answer would be: x*cos(125) + 3.44. It's one of the choices, but it's not the right answer. Thank you. Any help is appreciated. 
Re: Conversion Between Coordinate Systems
from reading the question it looks like there should be a diagram included...

Re: Conversion Between Coordinate Systems
Ah, my mistake. I did post an image but I guess I was the only one who could see the link since I was logged in to the school's online course website. I thought everyone else could access the picture. I've uploaded the picture on imageshack now and edited the first post.
Thanks for pointing that out. EDIT: for some reason I can't edit my first post. So here's the image. http://img111.imageshack.us/img111/6...ctice8qjp1.gif 
Re: Conversion Between Coordinate Systems
First, of course, you have to translate the origin. Let "p, q" represent a coordinate system with axes parallel to the x,y axes but with origin at x= 6, y= 3. Then p= x6, q= y 3.
Now, the u, v coordinate system is just the p,q system rotated by 35 degrees. In general, the p,q system rotated by [itex]\theta[/itex] degrees is given by [itex]u= p cos(\theta)+ q sin(\theta)[/itex] [itex]v= p sin(\theta)+ q cos(\theta)[/itex] 
Re: Conversion Between Coordinate Systems
Isn't it a 125 degree rotation since the x axis is pointing downwards? It has to rotate a total of 125 degrees.
According to the answer key, the answer is C. u = 1.74x + 10.44. I subbed p = x  6 and q = y  3 into the u = equation, but im not getting 1.74x at all. I got u = (x  6) cos (35) + (y  3)sin(35). 
Re: Conversion Between Coordinate Systems
the biggest problem i'm having looking at the possible answers is that none of them contain y, they should be of the form
[tex]u=xCos\theta +ySin\theta + a[/tex] sure, the question says with respect to x, but there's a constant at the end, you can't just ignore the y components... 
Re: Conversion Between Coordinate Systems
I found that strange as well
If i try just regular trial and error on the answers, it still doesn't make much sense to me. If i sub x = 6 into choice C, it gives u = 0. That doesn't really make sense on the diagram. 
Re: Conversion Between Coordinate Systems
I think I answered the question.
Here is my work. Can you guys please take a look and tell me if my work is right? http://img146.imageshack.us/img146/4...eviewq8tc0.jpg Instead of working with xy and uv, I limited it only to the x and u components From what the question is like, I think we are not working with the entire coordinate system at all. It is as if the y and v part of the coordinate systems do not exist at all. 
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