- #1
hp-p00nst3r
- 29
- 0
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.
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?
https://www.vista.ubc.ca/webct/RelativeResourceManager/Template/RspQ-Mech%202%20Review%20Quiz/220-practice-8q.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
I am not quite sure which equations are relevant but I think it has to do with linear transformations because of the rotating axes.
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.
Homework Statement
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?
https://www.vista.ubc.ca/webct/RelativeResourceManager/Template/RspQ-Mech%202%20Review%20Quiz/220-practice-8q.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
Homework 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.
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.