Posted by **Anonymous** on Sunday, December 9, 2012 at 6:44pm.

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 :) -
**Damon**, Sunday, December 9, 2012 at 8:10pm
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 :) -
**Damon**, Sunday, December 9, 2012 at 8:13pm
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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