<PRE><B>Question 977728</B>
Let east be positive x.
Let north be positive y.
He starts at (0,0).
1 mile south : (0,0) + (0,-1)=(0,-1)
3 miles east :(0,-1)+(3,0)=(3,-1)
5 miles north : (3,-1)+(0,5)=(3,4)
7 miles west : (3,4)+(-7,0)=(-4,4)
,
,
,
{{{drawing(300,300,-6,6,-2,10,grid(1),locate(-4.5,4.7,B),locate(0.4,0.8,A),circle(0,0,0.2),circle(0,-1,0.2),circle(3,-1,0.2),circle(3,4,0.2),circle(-4,4,0.2),line(0,0,0,-1),line(0,-1,3,-1),line(3,-1,3,4),line(3,4,-4,4),green(line(0,0,-4,4))))}}}
So then the distance from (0,0) to (-4,4) is,
{{{D^2=(0-(-4))^2+(0-4)^2}}}
{{{D^2=16+16}}}
{{{D^2=2*16}}}
{{{D=4sqrt(2)}}}{{{mile}}}</PRE>