Results 1 to 9 of 9

Math Help - Could use some help with a rhombus question

  1. #1
    Junior Member
    Joined
    Dec 2007
    Posts
    34

    Unhappy Could use some help with a rhombus question

    Sigh... I'm doing independant study to get some much needed math credits and I'm starting to get a feeling that the work material was designed for the sole purpose of testing my sanity. The key questions (they're like mini-tests) at the end of each lesson aren't so much fair as they are mind blowing curveballs from math- . It's like the people who wrote the lessons gave up at the end and figured that instead of thinking up challenging relevant questions, they'd just toss in a bunch of random nonsense that's impossible to answer given what's actually taught in the lesson.

    Oh well, enough complaining. I'm determined, and it's true that you can't keep a good man down. All that's needed is a little help from you, the hero. The one who's going to explain to me how I can prove quadrilateral W(-0.5, 1.5) X(4, 1) Y(3.5, 5.5) Z(-1, 6) is infact, a rhombus.
    Last edited by topsquark; January 24th 2008 at 05:19 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by mathdonkey View Post
    ... how I can prove quadrilateral W(-0.5, 1.5) X(4, 1) Y(3.5, 5.5) Z(-1, 6) is infact, a rhombus.
    Hi,

    a quadrilateral with 4 equal sides is a rhombus. Therefore calculate the length of the sides. If they are all equal then the quadrilateral is a rhombus.

    Hint: If you have 2 points P_1(x_1, y_1) and P_2(x_2, y_2) then the distance between these 2 points is calculated by:

    d(P_1P_2) = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Dec 2007
    Posts
    34
    Quote Originally Posted by earboth View Post
    Hi,

    a quadrilateral with 4 equal sides is a rhombus. Therefore calculate the length of the sides. If they are all equal then the quadrilateral is a rhombus.
    Really??? That's it?

    I looked at this site and assumed more would be needed!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by mathdonkey View Post
    Really??? That's it?

    I looked at this site and assumed more would be needed!
    I'm awfully sorry but math is not that complicated then you believe it is. Even the mentioned site states nothing but that the sides are all equal.

    Am I a hero now?
    Attached Thumbnails Attached Thumbnails Could use some help with a rhombus question-rhombus_eigensch.gif  
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Dec 2007
    Posts
    34
    Quote Originally Posted by earboth View Post
    I'm awfully sorry but math is not that complicated then you believe it is. Even the mentioned site states nothing but that the sides are all equal.

    Am I a hero now?
    Definately.

    I guess if all sides in a quadrilateral are equal then all the other properties must be true too?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644
    Hello, mathdonkey

    If you think that this is a difficult problem, you ain't seen nothing yet!


    Prove that quadrilateral: W(-˝, 1˝), X(4, 1), Y(3˝, 5˝), Z(-1, 6) is a rhombus.
    It's always a good idea to make a sketch . . .

    Code:
              Z   |
              *   |             Y
           (-1,6) |             *
                  |          (3˝,5˝)
                  |
                  |
                  |
                W |
                * |               X
           (-˝,1˝)|               *
                  |             (4,1)
          - - - - + - - - - - - - - - -
                  |

    Do you know what makes a quadrilateral a rhombus?
    . . That's right . . . it has four equal sides.

    Does WXYZ has four equal sides?
    . . How can we determine if: . WX \:=\: XY\:=\:YZ \:=\:ZW ?
    That's right . . . the Distance Formula.


    Go for it!

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by mathdonkey View Post
    Definately.

    I guess if all sides in a quadrilateral are equal then all the other properties must be true too?
    That's really a perfect guess.

    Probably you have found out that all sides of your quadrilateral have the same length with l = \frac12 \cdot \sqrt{82} \approx 4.5277
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Dec 2007
    Posts
    34
    Quote Originally Posted by Soroban View Post
    If you think that this is a difficult problem, you ain't seen nothing yet!
    Haha, now that I know how to do it, it's actually quite easy!

    I just over analyzed the problem. Blame it on my math phobia.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
    Posts
    293
    NB: After you’ve made your sketch, as Soroban did, you do not have to use the distance formula for all four sides! Just use the distance formula on any two adjacent sides, say WX and WZ. Then all you need to do next is show that the vectors \vec{\mathrm{WX}} and \vec{\mathrm{ZY}} are equal, i.e. the sides WX and ZY are equal and parallel. That is all.

    Everyone here seems so one-tracked about this problem that they seem to have forgotten that the rhombus has other properties too. Recall that a rhombus is a parallelogram. So another way of proving that a quadrilateral is a rhombus is to show that it is a parallelogram with equal sides. Showing that it has four equal sides is only way – but not necessarily the easiest way. Don’t be too narrow-minded when you are solving math problems.

    In fact, you can also show that it’s a rhombus without using the distance formula and messing around with squares and square roots at all. Once you’ve shown that \vec{\mathrm{WX}} and \vec{\mathrm{ZY}}, the fact that the other two sides are also equal and parallel will follow; hence WXYZ is a parallelgram. To show that it’s a rhombus, take the dot product of \vec{\mathrm{WY}} and \vec{\mathrm{XZ}} and show that it is 0, i.e. the diagonals are perpendicular. The rhombus is the only parallelogram whose diagonals intersect perpendicularly.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Geometry Question ( Rhombus )
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 6th 2010, 07:57 AM
  2. rhombus
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 11th 2010, 02:55 AM
  3. Dot Product Rhombus question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 6th 2009, 02:42 AM
  4. Need help with Rhombus Question
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 31st 2009, 02:53 PM
  5. help rhombus
    Posted in the Geometry Forum
    Replies: 1
    Last Post: October 12th 2007, 01:04 PM

Search Tags


/mathhelpforum @mathhelpforum