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Math Help - Parallelograms

  1. #1
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    Parallelograms

    OK, I am learning about Parallelograms at the moment and I am stuck on a certain problem....

    COORDINATE GEOMETRY Find the coordinates of the intersection of the diagonals of parallelograms PRYZ given each set of vertices.

    P(2,5) R(3,3) Y(-2,-3) Z(-3,-1)

    Please help me........
    Last edited by TheTruePhenom; March 23rd 2008 at 09:29 AM. Reason: Inappropiate language....
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by TheTruePhenom View Post
    OK, I am learning about Parallelograms at the moment and I am stuck on a certain problem....

    COORDINATE GEOMETRY Find the coordinates of the intersection of the diagonals of parallelograms PRYZ given each set of vertices.

    P(2,5) R(3,3) Y(-2,-3) Z(-3,-1)

    Please for the love of god help me........
    Watch your language!


    As for the answer, find the equation of the lines of 2 pairs of points, and then find where the two lines intersect.
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    Pardon my language, completely out of line....

    I dont understand by what you mean.....
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by TheTruePhenom View Post
    I dont understand by what you mean.....
    You have 4 points... Make 2 pairs of 2 points. Find the y = mx + c line between each of these pairs. You will then have the formulae of the diagonals. To find out where they intersect, set the formulae equal to each other.
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    Quote Originally Posted by janvdl View Post
    You have 4 points... Make 2 pairs of 2 points. Find the y = mx + c line between each of these pairs. You will then have the formulae of the diagonals. To find out where they intersect, set the formulae equal to each other.
    A happy Easter to you!

    In this case it's a little bit easier to use the property that the point of intersection of the diagonals must be the midpoint of the diagonals:

    If you have 2 points P_1(x_1, y_1) and P_2(x_2, y_2) then the midpoint has the ccordinates:

    M_{P_1 P_2}\left(\frac{x_1+x_2}2,\frac{y_1+y_2}2,\right)

    M_{PY}\left(0,1\right)
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    Bar0n janvdl's Avatar
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    Quote Originally Posted by earboth View Post
    A happy Easter to you!

    In this case it's a little bit easier to use the property that the point of intersection of the diagonals must be the midpoint of the diagonals:

    If you have 2 points P_1(x_1, y_1) and P_2(x_2, y_2) then the midpoint has the ccordinates:

    M_{P_1 P_2}\left(\frac{x_1+x_2}2,\frac{y_1+y_2}2,\right)

    M_{PY}\left(0,1\right)
    A happy Easter to you too, Earboth!

    (I always take the long way... Not because I'm hardworking, just because I fail to see the shortcut)
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  7. #7
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    Quote Originally Posted by TheTruePhenom View Post
    Pardon my language, completely out of line....

    I dont understand by what you mean.....
    You don't need "for the love of anything" especially as it may offend some
    of our uses unnecessarily.

    Ron:
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    I think I have the hang of it. I was using the slope formula instead of the midpoint formula and that got me all twisted around.....

    How about things like these...

    What about something of this extent....

    COORDINATE GEOMETRY Determine whether a figure with the given vertices is a parallelogram. Use the Method INdicated:

    P(-5,1) S(-2,2) F(-1,-3) T(2,-2) ; Slope Formula...
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  9. #9
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    Remember that a parallelogram is defined by the fact that it has two pairs of parallel sides. NOW is the time for the slope formula - find the slopes of all four lines. If the slopes of each pair of opposite sides are the same, then you have two sets of parallel sides and, hence, a parallelogram.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mathnasium View Post
    Remember that a parallelogram is defined by the fact that it has two pairs of parallel sides. NOW is the time for the slope formula - find the slopes of all four lines. If the slopes of each pair of opposite sides are the same, then you have two sets of parallel sides and, hence, a parallelogram.
    we are given that it is a parallelogram, we don't have to prove that. we trust the people giving us our question ... ...ok. so i think drawing a rough sketch is good enough, then we will know what points to test using Earboth's method
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  11. #11
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    Quote Originally Posted by Jhevon View Post
    we are given that it is a parallelogram, we don't have to prove that. we trust the people giving us our question ... ...ok. so i think drawing a rough sketch is good enough, then we will know what points to test using Earboth's method
    I was referring to the question in the post immediately above mine - the original post was answered. The post immediately above mine, as you can see, is about proving that 4 given points are vertices of a parallelogram using the slope method.

    Thanks for the snark, though.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mathnasium View Post
    I was referring to the question in the post immediately above mine - the original post was answered. The post immediately above mine, as you can see, is about proving that 4 given points are vertices of a parallelogram using the slope method.

    Thanks for the snark, though.
    my bad!

    i didn't realize a second question was asked

    (jeez, i'm turning into an american with that "my bad" stuff!)
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TheTruePhenom View Post
    I think I have the hang of it. I was using the slope formula instead of the midpoint formula and that got me all twisted around.....

    How about things like these...

    What about something of this extent....

    COORDINATE GEOMETRY Determine whether a figure with the given vertices is a parallelogram. Use the Method INdicated:

    P(-5,1) S(-2,2) F(-1,-3) T(2,-2) ; Slope Formula...
    Quote Originally Posted by Mathnasium View Post
    I was referring to the question in the post immediately above mine - the original post was answered. The post immediately above mine, as you can see, is about proving that 4 given points are vertices of a parallelogram using the slope method.

    Thanks for the snark, though.
    Quote Originally Posted by Jhevon View Post
    my bad!

    i didn't realize a second question was asked

    (jeez, i'm turning into an american with that "my bad" stuff!)
    This is why new questions need to go in new threads.

    -Dan
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