Question 1044206: A group of people decided to go cross- country skiing and the group has decided to stop at a rest cabin located on the trail. What is the distance from the parking lot to the rest cabin, if they skied 3km west, 2km northwest, 3 km east and 4 km north to get to the cabin?
much much appreciated ..thanks for all your help
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 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
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