Question 600377
The Distance between two points is 

D=sqrt[(x1-x2)^2 + (y1-y2)^2]

so, first the x's

x1=(2sqrt3)/3                          x2=-(2sqrt3)/3

[(2sqrt3/3)-(-2sqrt3/3)]^2
[(2sqrt3/3)+(2sqrt3/3)]^2
[2(2sqrt3/3)]^2
4(12/9)
=48/9

y's
y1=sqrt5/4                      y2=sqrt5/2
[(sqrt5/4)-(sqrt5/2)]^2
[(sqrt5/4)-(2sqrt5/4)]^2
(-sqrt5/4)^2=5/16
finally......

sqrt[(48/9)+(5/16)]
=(sqrt813)/12