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A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (3,2). write the length L of hypotenuse as a function of x.

  • Math -

    Let the x-intercept of the line be (x,0)
    let the y-intercept of the line be (0,y)

    we have similar triangles, and by ratios ...
    y/x = 3/(x-2)
    xy - 2y = 3x
    y(x-2) = 3x
    y = 3x/(x-2)

    L^2 = x^2 + y^2
    = x^2 + [3x/(x-2)]^2
    = x^2 + 9x^2/(x^2 - 4x + 4)

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