Optimization problem, triangle

  • Thread starter roman15
  • Start date
  • #1
70
0

Homework Statement


a line passes through the point (1,1/8) 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?


Homework Equations


i came up with three slopes for this line
m1=-b/a m2=-1/8(a-1) m3=(1/8)-b
A(a,0) and B(0,b)


The Attempt at a Solution


well i tried using these equations to solve for a in terms of b and then use that in the distance equation, but when i differentiated i ended up with a cubic function and i could solve
then i tried looking at the problem using similar triangles and the breaking up the distance between them into two parts, but then i got that b was 1/8 and a was 1 which doesnt make sense

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
35,235
7,053

Homework Statement


a line passes through the point (1,1/8) 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?


Homework Equations


i came up with three slopes for this line
m1=-b/a m2=-1/8(a-1) m3=(1/8)-b
A(a,0) and B(0,b)


The Attempt at a Solution


well i tried using these equations to solve for a in terms of b and then use that in the distance equation, but when i differentiated i ended up with a cubic function and i could solve
then i tried looking at the problem using similar triangles and the breaking up the distance between them into two parts, but then i got that b was 1/8 and a was 1 which doesnt make sense
If the coordinates of A are (a, 0) and those of B are (0, b), the slope of the line is -b/a. Now find the equation of the line, which will give you a relationship between x and y.

Your problem is to minimize the distance between A and B, and the distance is sqrt(a2 + b2). Using the equation of the line, you can write the distance function in terms of one variable, and then use calculus to find the minimum distance.
 

Related Threads on Optimization problem, triangle

  • Last Post
Replies
2
Views
1K
Replies
3
Views
6K
Replies
1
Views
5K
Replies
13
Views
2K
Replies
7
Views
18K
Replies
3
Views
1K
Replies
24
Views
2K
Replies
6
Views
4K
  • Last Post
Replies
5
Views
611
  • Last Post
Replies
3
Views
720
Top