Question 44972
Use Pythagoras' Theorem {{{d^2=x^2+y^2}}} for right-triangles, where d is the distance between the two points, x is the distance along the x-axis and y is the distance along the y-axis.
The change in x is equal to {{{6*sqrt(5)-4*sqrt(5)}}} which is {{{2*sqrt(5)}}}.
The change in y is equal to {{{7-1)}}} which is {{{1}}}
Now use Pythagoras:
{{{d^2=(2*sqrt(5))^2+1^2}}}
{{{d^2=(4*5)+1}}}
{{{d^2=21}}}
{{{d=sqrt(21)}}}

Just like that!

I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam