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Angular coeficient

  1. Sep 21, 2012 #1
    1. The problem statement, all variables and given/known data
    What is the angular coeficient of a straight line that passes through (4,3), if it satifies x>0 and y>0, and it is one of the sides of a triangle with total area of 27 (units of area).

    calcule o coeficiente angular de um reta que passe por (4,3) de modo que a parte da reta no primeiro quadrante forma um triângulo de área 27 com os eixos coordenados positivos.


    2. Relevant equations
    I know that the area of a triangle is area = base * height/2 . I know the equation of the straigh line is y = aX + B, where "a" is what I am looking for. But I am stucked! I cant find a nice relation.



    3. The attempt at a solution

    I've tried to use the relation Area = 1/2 * D
    Where D is the determinant of a matrix with the 3 vertices of the triangle, with an aditional columns of "1". But, couldn't go any further... any ideas?
     
    Last edited: Sep 21, 2012
  2. jcsd
  3. Sep 21, 2012 #2

    LCKurtz

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    I assume the axes form the other two sides of the triangle. Write the equation of the line though ##(4,3)## with slope ##a##. Its ##x## and ##y## intercepts will give you the base and height in terms of ##a##. Then set the area, now in terms of ##a##, equal to 27 and solve for ##a##.
     
  4. Sep 21, 2012 #3
    Perfect! I got it. Thank you so much!

    I got a solution with two possibilities, a= -1.5, or a = -0.375.

    Thanks!!!
     
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