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Homework Help: If two vertices of a square on the same side AB are A(1,2) and B(2,4)...

  1. Jan 21, 2016 #1
    1. The problem statement, all variables and given/known data
    If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D?
    2. Relevant equations
    1. y-y1 = m ( x-x1)
    2. m=y1-y2 / x1-x2
    3. m1*m2= -1
    4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2)
    5. m=tanA
    6. If ax+by+c=0 then its parallel line is ax+by+k=0
    3. The attempt at a solution
    Equation of AB is can be found using formula 4 , then slope is found using formula 2 . Then slope of perpendicular is -1/m (formula 3) . Now perpendicular AD and BC can be found using formula 1 . Now CD is parallel to AB . I need to find CD .....The distance between AB and CD is root 5 (of course since distance between AB is root 5 and it is a square) ....Please tell me how to find the side CD .....and diagonals AC and BD ...
  2. jcsd
  3. Jan 22, 2016 #2


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    Compute the equation of the line AB.
    You can then easily write down the equations of the lines AD and BC (you gave the correct rules).
    Then you can locate C and D (two possible solutions) on these lines using the distance.

    Said differently: don't use words to describe a possible solution, just compute what you said.
    Last edited: Jan 22, 2016
  4. Jan 22, 2016 #3


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    Alternatively, if you have studied vectors you don't need to deal with equations of straight lines and their slopes. Start with ##\vec{AB} = \langle 1,2\rangle##. Can you write down a perpendicular vector of the same length? That would get you started.
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