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If he could walk directly from the back door to the barn door, he would walk 10.2 yards less.
First, let's define our coordinate axis, I will use north as the y-axis and east as the x-axis.
So let's assume that Loto begins at the point (0, 0).
Then:
- He moves 8 yards east, to: (8yd, 0)
- He moves 6 yards north, to: (8yd, 6yd)
- He moves 12 yards east, to: (20yd, 6yd)
- He moves 5 yards north, to: (20yd, 11yd)
So he walked a total of 8yd + 6yd + 12yd + 5yd = 33yd
So he just moves from (0, 0) to (20yd, 11yd), thus the displacement is:
So, if he could walk directly he would only walk 22.8 ft
The difference is:
33yd - 22.8yd = 10.2 yd.
He would walk 10.2 yards less if he could walk directly from the back door to the barn door.
If you want to learn more about displacements, you can read: