Help Needed: Finding Segment AB of Line Through (2,2)

[dsb_101]

Sorry..i posted this same question in another wrong section. This is the right one..

A line through the point (2,2) cuts the x- and y- axes at points A and B respectively. Find the Minimum length of the segment AB.

Im really stuck on this problem. I know that minimum lengh is when f'>0.

Could you guys give me a lift off here?

ty

 

[Tide]

HINT: The distance between the two axial points is $\sqrt {A^2 + B^2}$ and equation of a line passing through the indicated point is $y-2 = -\frac {B}{A} (x - 2)$.

 

[tacman]

Hi there,

No problem, I'm happy to help with this problem. To find the minimum length of the segment AB, we need to use a little bit of geometry and algebra.

First, let's draw a diagram to visualize the problem. We have a line passing through the point (2,2) and cutting the x- and y- axes at points A and B. We can label the coordinates of point A as (x,0) and the coordinates of point B as (0,y).

Now, we can use the distance formula to find the length of segment AB:

d = √[(x-0)^2 + (0-y)^2]
d = √(x^2 + y^2)

Since we want to find the minimum length, we can take the derivative of this equation with respect to x (or y) and set it equal to 0. This will give us the critical point, which will be the minimum length of segment AB.

d/dx = 2x = 0
x = 0

Substituting this value back into our original equation, we get:

d = √(0^2 + y^2)
d = y

So, the minimum length of segment AB is when y = 0, which means that point B is located at (0,0). This makes sense because the shortest distance between two points is a straight line, and in this case, the shortest distance between (2,2) and the x-axis is a straight line passing through the origin.

I hope this helps and good luck with your problem! Let me know if you have any further questions.