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Math -urgent :)

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Hello
A straight line passes through the point (1,27) and intersects the positive x-axis at the point A and the positive y-axis at the point B.Find the shortest possible distance between A and B..

Pleaase could you help me?
Thank you in advance

  • Math -urgent :) -

    y = m x + b
    when x = 0, y = B so b=B
    y = m x + B
    when y = 0, x = A
    0 = mA+ B
    so
    m = -B/A
    so
    y = -Bx/A + B
    when x = 1, y = 27
    27 = -B/A + B

    27 A = - B + BA
    27 A = B (A-1)
    B = 27 A/(A-1)
    dB/DA = 27 [ (A-1)-A] /(A-1)^2

    d^2 = A^2 + B^2
    d d^2/dA = 0 for min
    = 2 A + 2B dB/DA
    so
    0 = 2 A + 2B[ 27 [ (A-1)-A] /(A-1)^2

    0 = 2A(A-1)^2 - 54 B
    0 = 2A(A-1)^2 -54 [ 27 A/(A-1) ]

    27 [27/(A-1) ] = (A-1)^2

    27^2 = (A-1)^3 = 729
    so
    A-1 = 9
    A = 10 amazing. You take it from there.

  • Math -urgent :) -

    oh well curious now
    B = 27(10)/9 = 270/9 = 30
    d^2 = 10^2 + 30^2 = 1000
    d = 10 sqrt(10)
    or about 31.6

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