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Math Help - Rotation and Transformation of Axes

  1. #1
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    Exclamation Rotation and Transformation of Axes

    Hi,I have a question that I have problems with.It's my homework due Thursday.


    M1(9,-3);M2(-6,5).Bring the origin to M2 and rotate the system so that M1,M2 agrees with the direction of the new x axis.(tanθ=-8/15).

    I can't understand what I'm supposed to find as a solution.Why do I need to change the origin?Should I only show how I did it?Thanks in advance.(I'm not asking for having my hw done by sb else.I studied all weekend on this subject but I can't understand the question.)
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  2. #2
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    Rectangular to Polar Co-ordinates

    [quote=truevein;474315]Hi,I have a question that I have problems with.It's my homework due Thursday.


    M1(9,-3);M2(-6,5).Bring the origin to M2 and rotate the system so that M1,M2 agrees with the direction of the new x axis.(tanθ=-8/15).

    [This is simply a variation on pythagorus theorum. Firstly, by bringing the origin to M2 (that is to say applying +6 and -5 respectively to the co-rdinates of both M1 & M2) the resultant values for M1 are now also the difference values as follows;

    XM1-XM2=15 and YM1-YM2=-8

    From these you can define a bearing (or azimuth) from M2 to M1;

    TANθ=15/-8 so ATAN(15/-8)= -61.9275 (Decimal Deg)
    -68.8083 (Grads)

    Note now that your new bearing has simply swaped the X and Y difference values which means that the axis has rotated thro 90Deg (100Grad).

    TANθ=-8/15 so ATAN(-8/15)= -28.0725 (Decimal Deg)
    -31.1917 (Grads)

    Simply add the two calculated bearings and your result will be;

    -90(Degrees) or -100(Grads)

    And if you require a distance;

    SQRT(15^2 + (-8)^2) = 17

    which is the same as

    SQRT((-8)^2 + 15^2) = 17]
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  3. #3
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    Thank you so very much
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  4. #4
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    Thumbs up You're not alone!

    You're quite welcome. And don't worry about not getting to grips with the problem straight away. I currently have to spend quite some time on a regular basis explaining this and other plane geometry principals to graduate civil engineers at my office, so you're not alone. Feel free to ask the questions if you get stuck again.
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  5. #5
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    Thanks again!Then I can ask some other questions at the weekend-if you don't mind-I'll study again to fully understand it and there will absolutely be questions that I'll have problems with.
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