SOLUTION: How do you use the Pythagorean Theorem to find the distance between the pair of points A(0,0), B(6,8) ?

We want to find the length of the red line below




Now we draw a (green) horizontal line segment with
one end at A(0,0) and the other end exactly below
and vertically lined up with B(6,8) (actually the
point C(6,0))  Then we draw a (green) vertical line
segment upward from there C(6,0) to the point B(6,8): 




Now we have a right triangle ABC, and we are ready to call on
"ol' 'Thag"



We can see that  and that , so
upon substituting:







So now we know that AB is 10 units long.

We could convince ourselves that that line really is 10 units
long by taking a compass, placing the sharp point at A(0,0) and
the pencil point at B(6,8), and swinging a big arc and we see
that it cuts both axes at 10.

 


FYI, notice that we could have drawn a right triangle this 
way and gotten the same results:



Edwin