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Math Help - equation of line by rotation

  1. #1
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    equation of line by rotation

    Find the equation of the line obtained by the rotation of the line x + y − 4 = 0 by pi/4
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  2. #2
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    Rotated about any particular point ?
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  3. #3
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    sorry, forgot to mention by pi/4 around the origin counter-clockwise
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  4. #4
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    x+y-4=0\Rightarrow\ y=-x+4

    which means the line has an angle of -\frac{\pi}{4}
    relative to the positive side of the x-axis.

    However, it does not go through the origin as (0,4) is on the line.

    The rotated line can pass through the origin, if we write the rotated line as y=mx+c, finding "m" and setting c=0

    Is that what you are looking for ?
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  5. #5
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    We could take a point on the line and rotate the line at that point.
    We could rotate "around" the origin if the line is a tangent to the circle x^2+y^2=8
    since the given line is a tangent to that circle.

    We need clarification.
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