Question 264994
The midpoint should be *[Tex \LARGE \left(\frac{2a+h}{2} \ , \ \frac{2a+h}{2a(a+h)}\right)]



Distance:


I'll start where you left off.



{{{d=sqrt((a+h-a)^2+(1/(a+h)-1/a)^2)}}} Start with the given equation.



{{{d=sqrt((a+h-a)^2+(a/(a(a+h))-1/a)^2)}}} Multiply the first fraction by {{{a/a}}}



{{{d=sqrt((a+h-a)^2+(a/(a(a+h))-(a+h)/(a(a+h)))^2)}}} Multiply the second fraction by {{{(a+h)/(a+h)}}}



{{{d=sqrt(h^2+((a-(a+h))/(a(a+h)))^2)}}} Combine the fractions.



{{{d=sqrt(h^2+((a-a-h)/(a(a+h)))^2)}}} Distribute



{{{d=sqrt(h^2+(-h/(a(a+h)))^2)}}} Combine like terms.



{{{d=sqrt(h^2+h^2/(a^2(a+h)^2)))}}} Square the second term.



{{{d=sqrt((h^2a^2(a+h)^2)/(a^2(a+h)^2)+h^2/(a^2(a+h)^2)))}}} Multiply the first term {{{h^2}}} by {{{(a^2(a+h)^2)/(a^2(a+h)^2)}}}



{{{d=sqrt((h^2a^2(a+h)^2+h^2)/(a^2(a+h)^2))}}} Combine the fractions.



So the distance is {{{d=sqrt((h^2a^2(a+h)^2+h^2)/(a^2(a+h)^2))}}}