Find the distance between the pair of points and find the mi

Find the distance between the pair of points and find the midpoint of the segment having the given points as endpoints. (a, squareroot a) and (a + h, squareroot a + h)

Solution

Two points are : ( a , sqrta ) ( a +h , sqrt(a +h) )

distance = sqrt[ ( a + h - a)^2 + ( sqrt(a + h ) - sqrta )^2 ]

=sqrt[ a^2 + ( a +h - a - 2sqrt(a^2 +ah))

=sqrt(a^2 +h - 2sqrt(a^2 + ah) )

midpoint = [ (x1 +x2)/2 , (y1 +y2)/2 ]

= [ ( 2+h)/2 + ( sqrta + sqrt(a+h) )/2 ]