How Do You Find the Minimum Length of Segment AB in a Coordinate Plane?

[dsb_101]

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]

Haven't I seen this problem before? :)

 

[moose]

http://www.twilightus.net/adam/optimization.JPG
I think this image is self explanatory and should get you off to a good start.

BTW, this is only one way of doing it, and there are many!

Now you have one defined length, and you can get everything else with this, good luck!

 

[HallsofIvy]

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.
ty

No, you don't know that- that makes no sense because you haven't said what f is. It is also true that the minimum (or maximum) of any function occurs when the derivative of that function is equal[\b] to 0 (not > 0).

So first decide what function you want to minimize. One way to do that is to look at moose's picture and think about similar triangles. Another is to assume the x-intercept of the line is at (X, 0) (X is some unknown constant) and write the equation of the line.

Hint: Since length is always positive, length will be a minimum when (length)² is minimum.