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

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) (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
-----------------
Use b for a+h to save typing
-----------
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)

It doesn't simplify. I don't see the point of it.

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

Distance:

I'll start where you left off.

Start with the given equation.

Multiply the first fraction by

Multiply the second fraction by

Combine the fractions.

Distribute

Combine like terms.

Square the second term.

Multiply the first term by

Combine the fractions.

So the distance is
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