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Thread: rhombus question

  1. #1
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    rhombus question

    Question:
    The equations of two adjacent sides of a rhombus are   y= 2x + 4 ,  -\frac{1}{3}x +4. If (12,0) is one vertex and all vertices have positive coordinates, find the coordinates of other three vertices.

    My attempt:
    rhombus question-bos-1.jpgClick image for larger version. 

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    the other vertex i found is (0,4)

    the distance between (0,4) and (12,0) =  4\sqrt{10}
    the equation of the line that passes through (12,0) is   y = 2x -24
    the problem is how to form the other equation in order to find the other vertices


    please help
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  2. #2
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    Re: rhombus question

    Let $(x_1,y_1)$ and $(x_2,y_2)$ be the other two rhombus vertices.

    distance between $(12,0)$ and $(x_1,2x_1-24)$ is $4\sqrt{10}$

    distance between $(0,4)$ and $(x_2,2x_2+4)$ is also $4\sqrt{10}$

    check your solution by determining the slope between those two points ... what should it be?
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