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Math Help - Coordinate geometry

  1. #1
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    Coordinate geometry

    Given a straight line BD where point E lies on it.

    Coordinates B(0.5,3) and E(1,1)

    Find the coordinates of D given that BE : ED = 1:3 and the equation of the line BD is y=-4x+5
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  2. #2
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    Hello, Punch!

    Was that the original wording of the problem?
    It's written very badly.


    Given points B\left(\tfrac{1}{2},\:3\right) and E(1,\:1)

    Find the coordinates of point D so that BE : ED = 1:3
    Here's a back-door approach . . .

    Code:
                  
          B(,3)o - +
                 \  :
                d \ : 2
                   \:
              E(1,1)o - - - +
                     \      :
                      \     :
                       \    :
                     3d \   :
                         \  :
                          \ :
                           \:
                          D o

    Going from B to E, we moved \tfrac{1}{2} unit right and 2 units down.
    . . And we moved a diagonal distance d.

    Going from E to D, we want to move a diagonal distance 3d.
    . . Hence, we must triple our previous moves.


    From E, we move {\color{blue}\tfrac{3}{2}} units right and 6 units down.

    Therefore, point D is: . \left(\tfrac{5}{2},\;\text{-}5\right)

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  3. #3
    Junior Member mrmohamed's Avatar
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    Lightbulb

    Quote Originally Posted by Soroban View Post
    Hello, Punch!

    Was that the original wording of the problem?
    It's written very badly.

    Here's a back-door approach . . .

    Code:
                  
          B(,3)o - +
                 \  :
                d \ : 2
                   \:
              E(1,1)o - - - +
                     \      :
                      \     :
                       \    :
                     3d \   :
                         \  :
                          \ :
                           \:
                          D o
    Going from B to E, we moved \tfrac{1}{2} unit right and 2 units down.
    . . And we moved a diagonal distance d.

    Going from E to D, we want to move a diagonal distance 3d.
    . . Hence, we must triple our previous moves.


    From E, we move {\color{blue}\tfrac{3}{2}} units right and 6 units down.

    Therefore, point D is: . \left(\tfrac{5}{2},\;\text{-}5\right)
    HI all
    Excuse me Mr soroban
    what about Point D (-1/2 , 7 )????
    in my solution I found D(5/2 , -5 ) and D(-1/2 , 7 )
    mrmohamed
    Last edited by mrmohamed; May 3rd 2010 at 05:16 AM.
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  4. #4
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    Quote Originally Posted by Soroban View Post
    Hello, Punch!

    Was that the original wording of the problem?
    It's written very badly.

    Here's a back-door approach . . .

    Code:
                  
          B(,3)o - +
                 \  :
                d \ : 2
                   \:
              E(1,1)o - - - +
                     \      :
                      \     :
                       \    :
                     3d \   :
                         \  :
                          \ :
                           \:
                          D o
    Going from B to E, we moved \tfrac{1}{2} unit right and 2 units down.
    . . And we moved a diagonal distance d.

    Going from E to D, we want to move a diagonal distance 3d.
    . . Hence, we must triple our previous moves.


    From E, we move {\color{blue}\tfrac{3}{2}} units right and 6 units down.

    Therefore, point D is: . \left(\tfrac{5}{2},\;\text{-}5\right)
    Hi! its you again I have understood your workings and I knew this before I asked this question on MHF. However, I am still a little puzzled on how to present my workings...
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  5. #5
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    Hello, mrmohamed!

    What about Point D (-1/2 , 7 )?

    That point is also correct . . . Good work!


    Silly me . . . I assumed directed distances,

    . . as in . \overrightarrow{BE} : \overrightarrow{ED} \:=\:1:3

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  6. #6
    Junior Member mrmohamed's Avatar
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    Lightbulb

    Quote Originally Posted by Punch View Post
    Given a straight line BD where point E lies on it.

    Coordinates B(0.5,3) and E(1,1)

    Find the coordinates of D given that BE : ED = 1:3 and the equation of the line BD is y=-4x+5
    HI all

    with my best wishes
    mrmohamed
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  7. #7
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    Thanks! but in the solution sheet shows only point is: \left(\tfrac{5}{2},\;\text{-}5\right) and the marks allocated to this question is probably only 2-3... judging from the long workings, perhaps your working is a more elaborated one compared to what is required of me?
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