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Math Help - Coordinate Geometry

  1. #1
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    Coordinate Geometry

    I am not able to solve this problem of Book 'The Element of Co-ordinate of SL Loney'

    Find the equations of the two straight lines drawn through
    the point (0, a) on which the perpendiculars let fall from the point
    (2a, 2a) are each of length a.


    Thanx in advance
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  2. #2
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    Re: Coordinate Geometry

    Do you know the formula for the distance from a point to a line, i.e., the length of perpendicular in this case?
    Thanks from varunkanpur
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  3. #3
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    Re: Coordinate Geometry

    Hi,
    Emakarov has told you how to solve the problem. I recommend that you follow his hint and solve algebraically. However, here's a geometry/trigonometry solution:

    Coordinate Geometry-mhfgeometry56a.png
    Thanks from romsek and varunkanpur
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  4. #4
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    Re: Coordinate Geometry

    very elegant
    Thanks from varunkanpur
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  5. #5
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    Re: Coordinate Geometry

    Hello, varunkanpur!

    Find the equations of the two straight lines drawn through A(0,a)
    on which the perpendiculars from the point B(2a,2a) are each of length a.
    Code:
          |     D
          |      *
          |     /   * a
          | 2a /       *    B
          |   /           *(2a,2a)
          |  /        *   :
          | /     *       :a
       A  |/@ * @         :
     (0,a)* - - - - - - - * - -
          |      2a       :C
          |               :
          |               :
      - - * - - - + - - - + - - -
          |       a      2a
          |
    We have: ∆ABC: AC = 2a, BC = a.

    We see that one line is: .y = a


    Reflect ∆ABC over AB so that: ∆ABD ≅ ∆ABC.
    Let θ = /BAC = /BAD.

    The slope of AB is: .tanθ = 1/2

    . . . . . . . . 2tanθ . . . . . .2(1/2) . . . . .1 . . . . 4
    tan2θ .= .----------- .= .---------- .= .---- .= .--
    . . . . . . . .1 - tan2θ . . . 1 - (1/2)2 . . .3/4 . . . 3

    The other line is: .y = (4/3)x + a
    Thanks from varunkanpur
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  6. #6
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    Re: Coordinate Geometry

    why repost what johng has already posted?
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  7. #7
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    Re: Coordinate Geometry

    Thanx for helping me and taking plains in solving the problem.
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