transformation

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what is the image of (1,-6) for a 90 degree counterclockwise rotation about the origin?

i guess it is (-1.6) is it?

  • transformation -

    That point is in quadrant 4, down to the right.(1 unit right of -y axis and 6 down)
    Spin it 90 degrees and it ends up above the x axis a distance 1 and a distance 6 right of the origin
    so I get
    (1,6)

  • transformation -

    no,
    did you make a sketch?
    I see it as (-6,-1)

    Proof: slope of original line = (-6-0)/(1-0) = -6
    slope of new line = (-1-0)/(-6-0) = 1/6

    they are negative recipricals so they form a 90º angle
    also you can verify that their lengths are the same.

    btw, are you using a rotation matrix ?
    what grade level is this in ?

    R(theta)=
    │costheta -sintheta │
    │sintheta costheta] │

  • transformation -

    i am in grade 11 but this stuff is from grade 10. i am a new student and have not studied it back in my country. the paper is due tomorrow and i don't have a clue how to do it.... the substitute handed us the paper today. so i cannot even ask my teacher till tomorrow....

  • transformation -

    your best bet might be to make a sketch on graph paper, and use your intuition.
    Notice that the x and y values contain the same numbers, except their signs might have switched as well as their positions, (-1,6) became (-6,-1)

    in general (a,b) becomes (-b,a) after a 90º counter-clockwise rotation and (b,-a) for a clockwise rotation.

  • transformation -

    thank you so much....i think i got it. thanks again!!!

  • transformation -

    Sorry, I made a typo
    one up and 6 right is
    (6,1)

    which you can also get by he matrix operation
    0 -1
    1 +0
    times your (1,-6) vector

  • transformation -

    Damon, I think she wanted to rotate counter-clockwise, you went clockwise

  • transformation -

    Damon, I apologize
    You went the correct way, I messed up and went the wrong way.

  • transformation -

    thank you both....so the correct answer is (6,1) Thanks!!! :)

  • transformation -

    I cheated and checked the matrix in my thick math book :)

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