1. ## Line Distance

A line passes through the points $({1,\dfrac{1}{8}})$ and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B?

2. Originally Posted by polymerase
A line passes through the points $({1,\dfrac{1}{8}})$ and intersects the positive x-axis at the point A and the positive y-axis at the point B. What is the shortest possible distance between A and B?
Suppose the point $B$ is $(0, b)$, then the line is:

$
y=\frac{1/8 - b}{1}x + b
$

and this meets the x-axis at $A = (-b/(1/8 - b),0)$

Now you can find the distance between $A$ and $B$ as a function of b.

Then find the $b$ which gives the minimum for this distance and the corresponding distance.

RonL

3. Originally Posted by CaptainBlack
Suppose the point $B$ is $(0, b)$, then the line is:

$
y=\frac{1/8 - b}{1}x + b
$

and this meets the x-axis at $A = (-b/(1/8 - b),0)$

Now you can find the distance between $A$ and $B$ as a function of b.

Then find the $b$ which gives the minimum for this distance and the corresponding distance.

RonL
I don't get how you obtain the part where you said that it meets the x-axis at $A = (-b/(1/8 - b),0)$....