SOLUTION: find the distance between the pair of points and find the midpoint of the segment having the poinits as endpoints. (a, 1/a) and (a+h, 1/a+h) /= divided by I figured out the midp

Algebra ->  Equations -> SOLUTION: find the distance between the pair of points and find the midpoint of the segment having the poinits as endpoints. (a, 1/a) and (a+h, 1/a+h) /= divided by I figured out the midp      Log On


   

Question 264994: find the distance between the pair of points and find the midpoint of the segment having the poinits as endpoints. (a, 1/a) and (a+h, 1/a+h) /= divided by
I figured out the midpoint (2a+h/a, 2a+h/2a(a+h) but I am having trouble with the distance: I got this far, I don't know what to do next.
d= square root (a+h-a)^2+ 1/a+h-1/a)^2
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the distance between the pair of points and find the midpoint of the segment having the poinits as endpoints. (a, 1/a) and (a+h, 1/a+h) /= divided by
I figured out the midpoint (2a+h/a, 2a+h/2a(a+h) but I am having trouble with the distance: I got this far, I don't know what to do next.
d= square root (a+h-a)^2+ 1/a+h-1/a)^2
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Use b for a+h to save typing
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d^2 = (a-b)^2 + (1/a - 1/b)^2
d^2 = (a-b)^2 + ((b-a)/ab)^2
Using b didn't help much
d^2 = h^2 + h^2/((a*(a+h))^2
d^2 = h^2 + h^2/(a^2*(a+h)^2)
d^2 = h^2*((a^2*(a+h)^2 + 1)/(a^2*(a+h)^2)
d+=+h%2Asqrt%28%28a%5E2%2A%28a%2Bh%29%5E2+%2B+1%29%2F%28a%5E2%2A%28a%2Bh%29%5E2%29%29
It doesn't simplify. I don't see the point of it.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The midpoint should be


Distance:

I'll start where you left off.


d=sqrt%28%28a%2Bh-a%29%5E2%2B%281%2F%28a%2Bh%29-1%2Fa%29%5E2%29 Start with the given equation.


d=sqrt%28%28a%2Bh-a%29%5E2%2B%28a%2F%28a%28a%2Bh%29%29-1%2Fa%29%5E2%29 Multiply the first fraction by a%2Fa


Multiply the second fraction by %28a%2Bh%29%2F%28a%2Bh%29


d=sqrt%28h%5E2%2B%28%28a-%28a%2Bh%29%29%2F%28a%28a%2Bh%29%29%29%5E2%29 Combine the fractions.


d=sqrt%28h%5E2%2B%28%28a-a-h%29%2F%28a%28a%2Bh%29%29%29%5E2%29 Distribute


d=sqrt%28h%5E2%2B%28-h%2F%28a%28a%2Bh%29%29%29%5E2%29 Combine like terms.


d=sqrt%28h%5E2%2Bh%5E2%2F%28a%5E2%28a%2Bh%29%5E2%29%29%29 Square the second term.


Multiply the first term h%5E2 by %28a%5E2%28a%2Bh%29%5E2%29%2F%28a%5E2%28a%2Bh%29%5E2%29


d=sqrt%28%28h%5E2a%5E2%28a%2Bh%29%5E2%2Bh%5E2%29%2F%28a%5E2%28a%2Bh%29%5E2%29%29 Combine the fractions.


So the distance is d=sqrt%28%28h%5E2a%5E2%28a%2Bh%29%5E2%2Bh%5E2%29%2F%28a%5E2%28a%2Bh%29%5E2%29%29