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.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

An x-y coordinate system is shown below. A second system, u-v, is also shown. What is the relationship between the u-coordinate and the x-coordinate?

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 (x-6) 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.

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# Conversion Between Coordinate Systems

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