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Math Help - find the coordinate

  1. #1
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    find the coordinate

    hi,

    this is my question:

    the points A(1,2), B(3,5), C(6,6) and D form a parallelogram. Find the coordinates of the mid point of AC. use your answer to find the coordinates of D.

    firstly i have found the mid points of AC which=(7,8)

    secondly i don't really know how to use (7,8) to find the D coordinate.

    Lastly i would really appreciate some help please, but could you really explain it so i understand!

    thanks!
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  2. #2
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    Re: find the coordinate

    Quote Originally Posted by andyboy179 View Post
    hi,

    this is my question:

    the points A(1,2), B(3,5), C(6,6) and D form a parallelogram. Find the coordinates of the mid point of AC. use your answer to find the coordinates of D.

    firstly i have found the mid points of AC which=(7,8) ... and this would be incorrect

    secondly i don't really know how to use (7,8) to find the D coordinate.

    Lastly i would really appreciate some help please, but could you really explain it so i understand!

    thanks!
    midpoint formula ...

    (x_m,y_m) = \left(\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2}\right)

    Once you find the correct midpoint of AC, note that it is also the midpoint of BD because the diagonals of a parallelogram bisect each other.
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  3. #3
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    Re: find the coordinate

    so the correct midpoint now would =(3.5,4) however what would i do after this to find the coordinates of D?
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  4. #4
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    Re: find the coordinate

    Quote Originally Posted by andyboy179 View Post
    so the correct midpoint now would =(3.5,4) however what would i do after this to find the coordinates of D?
    once again ...

    Once you find the correct midpoint of AC, note that it is also the midpoint of BD because the diagonals of a parallelogram bisect each other.
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  5. #5
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    Re: find the coordinate

    i don't understand! i know that (3.5,4) is also the mid point of BD but what would D be? would it be (3.5,4)? would i be (7,8)? could you please explain?!
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  6. #6
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    Re: find the coordinate

    Quote Originally Posted by andyboy179 View Post
    i don't understand! i know that (3.5,4) is also the mid point of BD but what would D be? would it be (3.5,4)? would i be (7,8)? could you please explain?!
    B(3,5) D(x,y)

    midpoint of BD ...

    (3.5,4) = \left(\frac{3+x}{2} , \frac{5+y}{2}\right)

    now ... what can you do with that?
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  7. #7
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    Re: find the coordinate

    do you mean, (3+x/2, 4+y/2) if so:

    3x/2= 1.5x
    4y/2= 2y
    (1.5,2) ?
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  8. #8
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    Re: find the coordinate

    Continuing on the method skeeter provided:
    The mid point of the line segment [AC] is (3,5;4) and it's also the midpoint of [BD] therefore:
    3,5=\frac{3+x}{2} and 4=\frac{5+y}{2}
    Solve this equations.
    Last edited by Siron; September 23rd 2011 at 12:22 PM.
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  9. #9
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    Re: find the coordinate

    Quote Originally Posted by Siron View Post
    Continuing on the method skeeter provided:
    The mid point of the line segment [AC] is (3,5;4) and it's also the midpoint of [BD] therefore:
    3,5=\frac{3+x}{2} and 4=\frac{4+y}{2}
    Solve this equations.
    3x/2= 1.5x
    4y/2= 2y
    (1.5,2) ?
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  10. #10
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    Re: find the coordinate

    Is \frac{3+1.5}{2}= 3.5? Is \frac{4+ 2}{2}= 4? I have no idea how you could possible get that. Have you never solved equations before? Start by multiplying each side of both those equations by 2.
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  11. #11
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    Re: find the coordinate

    6+x/2, 8+y/2
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  12. #12
    MHF Contributor Siron's Avatar
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    Re: find the coordinate

    What you wrote now is not even an equation ...
    If you have to solve:
    3,5=\frac{3+x}{2}
    Like HallsofIvy said, first multiply both sides with a factor 2, therefore we get:
    2(3,5)=2\left(\frac{3+x}{2}\right)
    \Leftrightarrow x=...

    Do this also for the other equation to find y
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  13. #13
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    Re: find the coordinate

    oh sorry i mis read, i didn't see 3.5=!

    7=3x
    7/3= 2.3
    2.3=x
    -2.3 from each side x=-2.3?
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  14. #14
    MHF Contributor Siron's Avatar
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    Re: find the coordinate

    You probably mean:
    7=3+x \Leftrightarrow x=4
    ?

    What do you get for y?
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  15. #15
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    Re: find the coordinate

    indeed, for y i got 3 so al together D=(4,3)
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