SOLUTION: Alex jogged 8 miles due north, then turned due west and jogged 6 more miles. How many miles is Alex from his starting point? (shortest distance)

Question 439668: Alex jogged 8 miles due north, then turned due west and jogged 6 more miles.
How many miles is Alex from his starting point? (shortest distance)

Found 2 solutions by stanbon, richard1234:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Alex jogged 8 miles due north, then turned due west and jogged 6 more miles.
How many miles is Alex from his starting point? (shortest distance)
---------------
Draw the picture:
Use Pythgoras
distance = sqrt(8^2+6^2)
----
d = sqrt(64+36)
-----
d = sqrt(100)
---
distance = 10 miles
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Cheers,
Stan H.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We can assign (0,0) to be Alex's starting point, and let be two vectors corresponding to his motion. If Alex goes 8 miles north, we can say this vector is given by , and going 6 miles west can be given by (we assume west/east correspond with the x-axis with west is negative, etc.). We can add the two vectors to get

, in which the magnitude (displacement) is equal to .

I used vectors because if you were given a problem where, say, Alex went 17 miles north-northeast at some angle, then 10 miles southwest at another angle, it would be best to use vectors.
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