Question 1044206
Use the coordinate system.
Start at the origin and go to (-3,0)
Then go 2 km NW.  This is sqrt(2) unit to left and sqrt (2) unit up.  Sum of the squares is 2+2=4, and square root of 4 is 2.  The new coordinate is (-3-sqrt(2),sqrt(2))
3 km east and the coordinate is (-sqrt(2), sqrt (2))
4 km north and the final coordinate is (-sqrt(2), sqrt (2)+4))
The distance is the sqrt of the sum of the squares, using the distance formula--subtracting 0 from each doesn't change that.
sqrt (2+16+8 sqrt(2)+2)=sqrt(20+8 sqrt(2))
numerically, that is 5.60 km