Question 198099
Imagine they're on the xy-plane, and they start off at (0,0)
6 blocks north puts them at (0,6)
10 blocks west puts them at (-10,6)
4 blocks north puts them at (-10,10)
The problem wants the length from (0,0)
to (-10,10)
The general formula is:
{{{d = sqrt((x[2] - x[1])^2 + (y[2] - y[1])^2)}}}
I'll say 
(x1,y1) = (0,0)
(x2,y2) = (-10,10)
{{{d = sqrt((-10 - 0)^2 + (10 - 0)^2)}}}
{{{d = sqrt(100 + 100)}}}
{{{d = sqrt(200)}}}
{{{d = 10*sqrt(2)}}}
{{{d = 14.142}}}blocks
The 1st path was {{{6 + 10 + 4 = 20}}} blocks
{{{20 - 14.142 = 5.858}}}
The direct path is 5.858 blocks shorter