1. ## Line Distance

A line passes through the points $\displaystyle ({1,\dfrac{1}{8}})$ 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 $\displaystyle ({1,\dfrac{1}{8}})$ 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 $\displaystyle B$ is $\displaystyle (0, b)$, then the line is:

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

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

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

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

RonL

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

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

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

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

Then find the $\displaystyle b$ 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 $\displaystyle A = (-b/(1/8 - b),0)$....